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scenario:
The battle takes place in a quarter mile in diameter, flat concrete, circle arena.
Both the Tyrannosaurus Rex and the animal are filled with bloodlust, and will not flee.
Rules:
To be a winner, the animal must still be alive with non-fatal injuries.
The moment the Tyrannosaurus is dead, the other animal is the winner, if it passes the first rule.
Exploiting the material properties of your arena and a loophole in the rules I’m going to have to go with everyone’s favourite indestructible critter:
The reasoning behind this is simple: your arena has no food, no water, and no shelter. Much like the Hunger Games this isn’t a matter of who is the best killer, it matters who is the best survivor.
At less than half a millimetre a Tardigrade will be utterly invisible on the concrete. Unless the concrete is polished it will probably fall into a microscopic bump and just stay there. It can’t see the T-Rex to attack it, but that’s OK: The T-Rex can’t see it either. From here it’s just a matter of time.
Tardigrades have a neat trick where they suspend their metabolism and basically become indestructible. They’ve been frozen, boiled, crushed, exposed to vacuum, exposed to hard radiation, dehydrated, drowned and.. well.. basically everything.
Most of the time all it took was a splash of water and they’d be back on their feet.
So: under the baking sun in your arena the Tardigrade will dehydrate, enter this cryptobiotic state (cool name) and just... be.
Meanwhile the T-Rex will start to dehydrate. This will be the thing that kills them unless it rains. If it rains they’ll now be standing in a pool of water. The Tardigrade won’t care about this. It’ll still be having a nap. Then the T-Rex will stomp about for weeks before eventually starving to death.
Now for the rule loophole: The victor must still be alive and have no fatal injuries when the T-Rex is dead. This automatically means the Tardigrade has won. Simply by going to sleep for a bit.
Oh, and if you’re wondering how long the Tardigrade could keep this up if the T-Rex was fed? The T-Rex would die of old age before the Tardigrade even noticed. They can sleep for centuries and still be revived.
The only wrinkle in this is whether or not you count the tardigrade’s suspended animation as still being alive. It can certainly be revived, but technically speaking? If you just left it alone at the bottom of a concrete well it might never wake up again.
Which would be a disappointing end to an already disappointing fight.
A colony of army ants.
You have several problems, most people underestimate the size of a T-rex, a full grown Siberian tiger's entire body is smaller than just a T-rex's head. Very few living animals have a way to kill a T-rex, just due to how far the vitals are from the surface. Several people have mentioned the brain but they don't realize how deep a T-rex brain is inside its skull. There is over a foot of bone and muscle in the way. As you can see below, a T-rex brain is not placed like a modern mammal or bird's brain. Worse: it is encased in a brain case of several inches of bone once you get to it. There just is no comparison with a modern terrestrial animal. Even if a T-rex was paralyzed for hours I doubt a tiger or pack of hyena could even injure its brain (although they could certainly kill it in that time frame).
Rhino and elephants have weapons that could produce a fatal injury but a T-rex evolved to fight a thing of a similar or bigger size with similar or better weapons that are actually good at being that size. So they have a chance but not much of one.
For the few land animals that could actually get venom through a T-rex's hide they are not venomous enough to kill before the T-rex could crunch them many times over. There are a few marine animals more than venomous enough but nothing that lives on land.
The only thing left is something small enough to attack soft tissue without being able to be shook of scraped off easily. An ant swarm comes to mind, many biologists treat a colony as a single super organism. A T-rex will have a very hard time killing ants once they get on it, and ant can attack soft tissue like the nasal passages until the T-rex bleeds out. Even then it will be close, rubbing and shaking will whittle down the ant numbers and the ants still have to get one the T-rex. So it will be a race between how much damage they can do vs how many the T-rex can kill. I would get the ants better odds but just barely because it will be hard to kill every last ant.
The Australian Magpie.
As others have pointed out, it's hard to imagine any animal beating the T-Rex head-on. I think in this scenario you really have to think about what the T-Rex is bad at. One thing that comes to mind is reaching over it's head, or defending itself from an attack from above, particularly against something as small and nimble as a bird.
An animal that could land on the Trex's head and attack its eyes could do some serious damage without leaving a lot of defence for the T-Rex. The Magpie's natural instinct to swoop will be valuable here as well. Once the eyes are pecked out, it's a question of whether a T-Rex will die of infection more quickly than a magpie will starve to death. I think the Magpie could win. Ok it's a long-shot.
A well fed vampire bat
Vampire bats are a very interesting group,especially the common vampire bat (Desmodus rotundus). They're one of the few bat species capable of running, can perform quick takeoffs on the ground by performing a quad launch, can find prey by their breathing and is used to stir its prey until its too tired. Their diet consists entirely of blood, which is why they need a good meal every 3 days at least.
A well fed vampire bat, being adapted as it is to deal with animals dozens of times its own size, could most likely get close to a win. With its size, I doubt the enraged t-rex would even feel it landing on its back to rest. It's ability to climb should be more than enough to keep it there and even if it's not, it can just fly away. It's speed and reaction time are enough to dodge the T-Rex's bite attacks, stomps and tail swipes (and it can always fly out of its range). It could stir the T-Rex until it falls asleep, provide several small wounds by finding the closest blood vessels to the surface like it does to its normal prey (as well as providing itself a replenishment in food and water) and then go for an eye. We'll then have a t-rex with one eye and several small wounds (I don't doubt it can cut, as vampire bats have one of the sharpest teeth in the animal kingdom, at times used to even shave the fur of large mammals to allow for a better bite) and a once again well fed bat. Repeat the process, mount on the now blind T-Rex (which also can't stop bleeding thanks to the draculin in the bat's saliva), feed on its blood until it inevitably dies of infection, dehydration and hunger and we have our beautiful winner.
The key here is that unlike other animals, the bat can most likely outlast it's competitor simply because it's too small and agile to be caught and its opponent can also work as its food source. Given their naturally stealthy nature, even if the bat did absolutely nothing other than staying on its back and securing a blood vessel with the heat sensing structures in its nose, it could just chill on the T-Rex's back drinking blood whenever it feels hungry (due to its diet they simply don't need water sources other than what's already in the blood they drink) while it waits until the T-Rex either starves or dehydrates.
Ratels and their closer relatives are the only animals crazy enough to engage in a 1 versus 1 against a T-rex...not even lions fight alone, and tigers only kill things weaker than them. And any other animal would just turn back and run away from a T-rex...there's no animal on earth that wouldn't crap themselves in fear when confronted by such a monster.
But what about snakes? Snakes are even afraid of humans, they'd probably die of a heart attack when a tyrannosaur is charging them, even if the T-rex is allergic to bees, the bee would die after stinging the dinosaur. And other poisonous insects don't have the guts or the strength to pierce the dinosaur skin in order to inject their poison, but even if they were able to pierce a dinosaur's skin,they would not have enough venom.
Only poisonous frogs have enough toxins to kill a tyrannosaur, but the frog would need to be eaten alive in order to kill the dinosaur.
Ratel and it's closer relatives are the only animals frequently engaging combat with other predators bigger, faster, smarter and stronger than them.
There are also accounts of wolverines ( the same family of Ratels) killing polar bears by biting their throat.
The way I see it, there's literary no other animal that would actually fight against a T-rex. And the only way your wolverin or ratel has to win is to get between the tyrannosaur legs without getting stomped, climb up and bite it's eyes out off the tyrannosaur skull. T-rex has no arms to defend itself, and once the ratel started climbing, the odds are in favor of the ratel.
The T-rex could try rolling on its back to fend off the ratel, but those animals are agile and the ratel could easily jump off before being stomped, and while the tyrannosaur is still on the ground, the ratel has an advantage reaching the enemy skull.
Could a ratel just bite a T-rex throat and suffocate it by leaching onto it for a few minutes? Probably, but the tyrannosaur would have some time to think about ways to kill the small ratel in those minutes.
If the ratel just bites off the T-rex eyes, everything becomes safer and the ratel could even reach deeper into the skull and eat their brains out.
Also a T-rex's eye is as big as a Ratel's head, so the small guy would have no problem jamming it's teeth through.
With the caveat that it is a bit unrealistic to expect neither animal to flee until death (but hey, we have a T Rex so who cares, its fun to think about), your best bet is a Jaguar. No living animal is going to be able to go toe-to-toe with a T-Rex in a pure contest of strength, it is simply too large and strong. However, Jaguars have incredibly powerful jaws, are adept climbers, have a lot of muscle packed into their frame, and are very agile. They also already prey upon large lizards, in that they have been known to kill crocodiles by driving their teeth through the skull into the brain cavity.
From the Wikipedia page:
A short and stocky limb structure makes the jaguar adept at climbing, crawling, and swimming. The head is robust and the jaw extremely powerful, it has the third highest bite force of all felids, after the tiger and the lion. A 100 kg (220 lb) jaguar can bite with a force of 503.6 kgf (1,110 lbf) at canine teeth and 705.8 kgf (1,556 lbf) at carnassial notch. This allows it to pierce the shells of armored reptiles and turtles. A comparative study of bite force adjusted for body size ranked it as the top felid, alongside the clouded leopard and ahead of the tiger and lion. It has been reported that "an individual jaguar can drag an 800 lb (360 kg) bull 25 ft (7.6 m) in its jaws and pulverize the heaviest bones".
Given its large advantage in maneuverability, I see the Jaguar avoiding the attacks by the Tyrannosaur (who can really only do damage by stomping or biting) until it can climb up its back, where it will kill the lizard by driving its powerful canines into its brain. Not only CAN the Jaguar win in this fight, but I think it would be likely to. The T Rex will be hard pressed to catch or really do any damage at all to this creature much smaller and lower to the ground than itself.
No other cat (or animal) combines agility, strength, and powerful jaws in the way the Jaguar does, making it uniquely qualified for this thought experiment. Gorillas have strength and climbing, not enough weaponry. Bears have strength and weaponry, not enough agility. Also, Jaguars are used to hunting solo, which Lions are not, and they boast better agility than the larger and stronger Tiger.
It is not thier bite that kills but the plethora of blood born illnesses that they carry with each bite. But as dangerous as they are to modern animals, they are much worse to the T-Rex. What makes the tick particularly deadly to the T-Rex is that the pathogens it carries have had an extra 66 million year of evolution to figure out how to overcome animal immune systems. While the "battle" happening outside the body would be so unbalanced that the t-rex would not even know that it is being attacked, what happens inside the body would be the equivalent to a modern army storming an encampment of neanderthals.
Mosquitoes may work even better for all the same reasons if you consider all terrestrial animals to be "land animals."
No animal can beat a T-Rex in an arena
I know, if you count in some loopholes like parasites or Tardigrades... Sure. But the question asks for an arena battle. Something that people would like to watch. So if we want a goliath vs. goliath fight we have some options like rinos, elephants or hippos. All of those somewhat come close to a triceratops but they lack one thing: They don't know how to protect themselves against such a large predator. The T-Rex evolved to kill large dinos. Dinos that fight back. Killing large animals is his nature. There is nothing, that can beat it today.
African Elephant
Since you waved the bloodlust of both contenders an african elephant charging frontaly could be faster in piercing the T-Rex' heart than that one to inflict deadly bite.
Arguments:
I think Homo sapiens sapiens could do it. Even full of bloodlust, the human can be crafty. Conserve water, run away and let the lumbering beast burn calories without water, and stick to the perimeter where T-Rex has to turn corners to catch the human.
Probably best to go with King Kong.
A gorilla is among the strongest animals on earth, it's smart, has a huge bite force (more than a lion or great white shark), it's fast and has hands with a grip strong enough to crush a crocodile.
If it can dodge the mouth it could rip those silly looking t-rex arms off and do a lot of damage while Mr. Rex bleeds out.
Best case scenario it uses it's speed, weight, and grasping hands to tip the t-rex on it's side, then rips off the little limbs and batters it until it dies.
Any animal that's fairly fast and strong enough to damage a T-rex might have a decent chance.
The reason dinosaurs got so big is because there was more oxygen in the air. Today we have a lower percentage, so the maximum size of an animal is less.
If you asume your T-rex doesn't die from the difference, it's going to have a hard time when it has to work for it. The more it has to move, the more oxygen it needs, the faster it's out of breath.
I agree with one of the big cats, like the Jaguar, as the obvious winner. Thoe Rex is big and strong, the cats are powerful, solitary hunters who can defend themselves well. I’ve seen even the cougar Go toe to toe with a bear and win. The big limitation T Rex has is his bitty arms. Big cats will see this vulnerability, leap onto T Rex’s back where they are virtually unassailable by the Rex. From there its a matter of doing injury to the neck and spine until he goes down. Yes, the cat. That would do it there.
