I think the closest example is Nazi Germany attacking the USSR and Imperial Japan attacking the USA. Afaik the Japanese were not as suicidal as it appears, they had a particular goal in mind and it was all going to hell anyway.
And, again afaik, the USSR was not respected as much and the Red Army was though to be a push over by both the Axis and Allies.
Now this is not an attempt to talk about WWII, obviously, just some context to why it is possible to have such a scenario.
And so my story begins with an alien fleet that appears in our solar system on a sunny, ok it's meaningless is space but let me have it, Saturday and starts approaching earth fast.
A week later an alien "invasion" is launched
So what is the aliens thinking?
First of all they are a splinter group from their "state" they are radicals and believe in their superiority over everything. And they did arrive with technology the likes of which we can only dream of.
They also estimated that since humans are already divided into rivaling nations. It's much easier to launch separate attacks on each state opposed to what would happen if we had one single unified military like they do.
The military operation had specific and clear goals. So their initial target Are:
Their ultimate goal of the attacks is not total annihilation but to weaken the collective human race enough so to bring them to the negotiation table so that a favorable agreement can be reached.
This agreement they want is just them getting lands to settle with absolute power over them and special statues among humans. Like they can't be trialed at our courts and so on. Which have a lot of historical bases.
I could not make them blind enough to believe they can destroy the human race.
Now they really want to destroy the military bases but when it comes to infrastructure they see the need for that later on, as they don't want to mess things up too much, so they won't focus on that heavily and won't utterly destroy them. Just enough attacks to cripple the country for a while.
Can't they just come in peace? No.
Why bother with earth in the first place? We are the only habitable planet they encountered, and having access to our own tech and infrastructure would actually give them a lot to work with. Because again they are not an arm of their state, they did not bring all the coolest toys with them from their own state. And so having a whole planet with more than 7 billion potential workers seems better than trying to settle in Mars.
They also see the subjugation of the humans as an important point in in validating their own believes and ideology.
What type of technology is available to them?
So far the most logical thing is a highly advanced ships with nearly unlimited power and large manufacturing capabilities. They have lot of drones and a crap ton of plasma and laser based weapons and vehicles. Most of which are controlled from their own ships by pilots or assisted computers, they don't have or like AIs.
The rest is up to you.
Their numbers can't be more than a few millions but that includes civilians so their actual military can't exceed half a million that if they put all capable males into it.
So when it comes to ground troops they don't have much. They use drones and their own tanks. Those tanks are obviously much stronger than ours but they can be taken out.
They don't actually have much of an air force, nor do they posses vastly powerful startship cannons. The air force can still be better than ours and still be decent. Their own ships are mostly armored and protected by shields for ship to ship attacks. But not top of the line invasion ships. This ties in with the fact they are a splinter group not the actual military arm of their race. So you if you want to add using their own ships for the attack do so but without making planet killer type of weapons.
Can they call support? Heck no.
Why focus on them? Because it's much easier to change the aliens than to introduce plasma tanks to humans with all the complexity that brings.
Do they have access to biological or chemical weapons or nukes? Initially they don't have them.
What is their military creed like? Mostly using overwhelming tech in the form of tanks and drones and so on to win the war.
So the focus is mostly on the type of vehicles they have and how to use them. But this would depend on the answer and I'm open to suggestions.
What is their biology like? Human like. Only more fragile and they detest manual labor and actually fighting.
Since they are space faring with vastly superior tech. I think they can turn the entire earth to glass if we wanted to, and thus the question and premise don't work! First they don't want to do that, second they actually have limitations. Also it's not fun.
Hopefully that's enough information.
This is getting long and so to sum it up they need to have a more advanced army, and initially do a lot of damage to our states but have their own "brilliant" plan fail within a time frame that I'm flexible to because it would depend on what you guy suggest.
And so I just want to focus on the answer to the main question and other points will have their own questions.
So. What is their overall military capability have to be in order to attack us but actually fail in achieving their goals?
Edit 1: to clarify the original idea is that they did not plan on our own invasion per say. They just escaped their own state and "happened" to find our little slice of heaven. So it would seem weird that they arrive with specific weapons or ideas to fight us.