Partial extension to this question: What kind of natural armor would stop bullets?
I was wondering what kind of jaw and tooth build would be able to break armor which can withstand 4 gigapascals to 25 gigapascals. This would have evolved naturally, as many creatures on this planet have very tough armor. The closer it is to the higher end of the pressure, the better.
This creature is a carnivore.
Conventionally, this predator will need short jaws, pyramid shaped teeth, and slow twitch muscles. Even if the predator can't crack the mantis shrimp style armor, it doesn't need to penetrate to be effective. Crushing the armor by causing the sides to snap may be more effective than trying to punch through.
Making frontal assaults on super strong defenses is exactly what Sun Tzu advises you not to do. Attack sideways. In the days of WW2 tank warfare, the British used a type of ammunition called HESH - High Explosive Squash Head. The idea was that a plastic explosive would hit armor plate, flatten out against the plate then explode. The explosion caused a huge pressure wave to travel through the armor plate. When the pressure wave hit the back side of the armor, it would exceed the structural strength of the steel and cause splinters of armor to go whizzing around the inside of the tank.
The point of HESH wasn't to punch a hole through the armor as much as use the armor itself to do damage. However, with the introduction of spall liners and spaced armor, HESH became less useful. But this predator's prey won't have spaced armor or spall liners.
To use this HESH idea, build a predator with quick-closing thick jaws with teeth shaped like hammers. If the jaws close fast enough, they'll do the same thing that HESH rounds do to tanks. Little bits of high speed armor fragments from the inner side of the armor will go whizzing through organs, muscles, bone, and blood vessels. Even if this doesn't kill the prey, it will seriously impede their ability to retaliate.
Medievel armor and weapons fell into a very similar situation. Plate armor is basically impenetrable by blades of any kind. In response, knights and infantry started equipping war-hammers to bludgeon the enemy knights to death. Armor won't help you much against percussion attacks; you need extra padding and extra space between the armor and the juicy bits inside.
Let's take this from another angle. Turns out Earth-life has done much of the work for us, giving us a menu of options:
Crocodile Model
Clearly this armor is tough. Probably too tough to bite straight through it. So pure biting force is not what you need. After all, the armor has to connect to the body, right? That's the weak link your predators need to exploit.
I'm thinking about something like a crocodile, which grabs onto a limb or piece of flesh and then spins rapidly until the torque rips the desired piece straight from the body. Whatever connective tissue is holding the armor onto the body will eventually fail. So you need high pressure bite; not enough to defeat the armor, but enough to hold on through the whipsawing action required to rip the armor off the flesh.
Starfish Model
Starfish face the same problem. To wit, armor on clams, which they can't defeat. So they simply shrug (with five limbs, you gotta see it), extrude their stomachs, and digest whatever they can reach until the shell pops open.
Lamprey model
Lampreys don't really typically deal with armor per se, but their form factor would be good to challenge an armored creature. Imagine your predator might have a long snout which can dig around to find joints or gaps, then push into the prey to eat it hollow from within.
Update -- More Love from the Animal Kingdom
Spider Model
Many spiders are patient, and don't really enjoy the notion of sucking solid organs through a straw. So they inject their victims with a powerful dissolving agent and wait awhile for the brew to marinate. (This is easier to do with exoskeletal creatures who come with a built-in "container", but workable with other creatures too) Then they can slurp up the nice liquefied insides with little trouble.
Anaconda Model
"Chew? You expect me to chew my food? Who has time for that?" This is the motto of snakes worldwide. Who needs to puncture the armor when you can swallow your prey kit and kaboodle? Then you can take a six-month nap while you digest it. Note that the constrictor model may be even better, as armor designed to face up to frontal threats may well fail under compression from the sides...
Eagle Model
I've seen videos of birds of prey picking up turtles and dropping them from great heights, thus cracking their shells. You might be able to work with this. Also, I've seen video of eagles knocking goats off a cliff, showing that this works with larger prey. It's a little cold, but ... birds, y'know. Savage dinosaurs the lot of 'em, they'd slay us all if they could.
Update -- Okay, the gloves come off
Mantis Shrimp Model
Invincible armor, huh? This has been mentioned in another answer, but let's highlight it some more. These shrimp "cock" their punching arms compressing a flange which wants to spring back hard. So when they strike, they get momentum from muscle as well as from the flange springing back into shape. They strike with the speed of a rifle bullet:
When Sheila Patek, a researcher at USC Berkeley, tried to study these heavy-hitters on video, she hit a snag. “None of our high speed video systems were fast enough to capture the movement accurately” she explained.
Turns out the strike is so fast it leaves a vacuum in the water, which creates heat and light when it collapses. If a predator using this principle hits the armor, that may well be enough to defeat it. Even if not, the transmitted shock will be enough to ruin the armored creature's day.
Here is a meditative picture to help:
Limpet Model
Thanks to mlibby in comments, we have become aware of the mighty Limpet, whose teeth are so strong that the limpets accidentally swallow rock fragments they tear free while scraping rocks for food. From BBC.com:
The teeth are made of a mineral-protein composite, which the researchers tested in tiny fragments in the laboratory.
They found it was stronger than spider silk, as well as all but the very strongest of man-made materials. [...] fibres, consisting of an iron-based mineral called goethite, are laced through a protein base in much the same way as carbon fibres can be used to strengthen plastic
Your predators can have teeth made of this same material and just rasp through the armor. I'll leave you with a close-up of limpet teeth, to ensure screaming nightmares for months...
Just a big, strong jaw. It's only a matter of being stronger than the armor.
Teeth matter a little. Sharp teeth let you get more pressure from the same force. The teeth need to be strong enough to not break. If the goal is to pierce the armor, then you want long, strong, sharp teeth. Like a saber tooth tiger. If the armor is easier to crush than pierce, then you want stout teeth with many sharp points of contact. Like a crocodile. Or a moose.
But the strength of the jaw matters more than the teeth. At a certain point it's just about biting harder. To exert a large force, you need to be able to actually get your mouth around the target. That means your mouth needs to open wide enough to get on both sides of your target. And big muscles to close the jaw. Strength in biology is quite often about bigger muscles and thicker bones rather than better design.
This creature is in serious trouble. The strongest bite known to man is the crocodile's, at 0.02 GPa (https://news.nationalgeographic.com/news/2012/03/120315-crocodiles-bite-force-erickson-science-plos-one-strongest/).
You are talking about two or three orders of magnitude more, which is a lot.
But not all is lost for your chomper. Consider the following possibilities:
Saw the armor instead of biting through it
If the material is extremely impact-resistant, we need to change the tool. I am not sure what would be scratch resistance of this armor, but I bet it can not be very high. This way, attacker can bite like a shark does, by sawing off the limbs instead of simply biting them off (like most predators do).
The attacker can have a large number of small triangular teeth which together act as a saw. Those teeth need to be only somewhat more scratch-resistant than the armor, and there is not much of a requirement for impact resistance.
Another approach is to go after the chinks in the armor
Predator can have long sharp claws (or beaks, or teeth) that penetrate between the armor plates and wring them apart. Some predators are adept at attacking shelled prey in that way.
Abrasive tooth on either a high-speed reciprocating jaw or on a rotary jaw. (The G'Kek species in David Brin's Uplift universe have rotary limbs.) Grind the armor away at a relatively fine scale, using tooth material which may be consumable or may be exceedingly hard (e.g. diamond or tungsten carbide), at least at the edges/faces of the grinder. Jackhammer / woodpecker jaw is a variation of this.
Hydraulic jaw; tooth can be grown or found (e.g. stones), jaw wraps entirely around prey, and teeth are pressed into the armor.
Water-hammer jaw; prey's armor is immersed in incompressible fluid and the predator causes the incompressible fluid to slam into the armor. Might find the weak spots in the armor which occur naturally due to the shape in which it's grown but which is not easily detected.
Liquid cavitation jaw; prey's armor is immersed in fluid which the predator causes to cavitate then flow against the armor where the bubbles collapse.
Abrasive liquid jet; predator pierces (or if the armor has an edge, slices) the armor by spraying it with high-pressure liquid full of microscopic bits of glass, i.e. plankton skeletons. May not be appropriate for biological creatures, but here's 2.5" thick steel being sliced slowly by water with abrasive: https://www.youtube.com/watch?v=LB0oT5AEJfA
Two opposed giant "piercer" teeth with a massive, strong jaw, like an upscaled snapping turtle. 
Each tooth is a pyramid shape and the point is hardness-enhanced with some secretion which is more hard than tough. Armor which is as strong as the tooth becomes prohibitively expensive for covering an entire animal, in terms of minerals or the ability to move.
Heat or cool the armor chemically right where the jaw/teeth are trying to bite into it. The jaw is as much an applicator for exotic chemicals (or high-power electric discharge) as it is for biting.
Glass-cutter and wedge/split the armor; basically using a small and hard tooth to make a shallow crack in the armor (which it is designed to tolerate - that's why it's so tough) then encouraging the crack to propagate in a destructive way, either by lifting the cracked edges of the top layer and applying the tooth to the next layer (possibly by a shaped tooth which can lever off of the layer(s) of armor it has already cut and bent away), or by grabbing the armor in multiple places and flexing it.
The probably best approach would be not to break the armour at all but to kill the prey. Doing so does not require breaking the armour since while the armour may withstand ridiculous pressure, the animal on the inside won't.
Once dead so the predator can be sure the prey won't bite him in the intestines, the predator can swallow it whole. Might take a week or two to digest, but who cares.
Whatever armour an animal has, it needs to be either partial or flexible in some way or the prey is unable to move at all, or, well... breathe. That means that no matter what, you can compress it, without the need to break it.
You don't even need excessive force if you rely on e.g. the prey breathing. Just do as some large snakes do: Hold tight, and every time the prey takes a breath, follow the motion and hold a little tighter. Only just, never release until there's no more movement for some minutes.
