The first few bosses in Axiom Verge don't pose too much of a threat, but some of the later ones may take a handful of tries to defeat. Nevertheless, here are some strategies for all bosses in the game.
Xedur likes to fly horizontally while he shoots a ton of projectiles. Luckily the projectiles are very slow - think of it as a manageable bullet hell section. Simply avoid the projectiles and shoot up at his tail. He also throws out timed explosives, but they take a while to explode. The explosives do a decent amount of damage, but avoiding them shouldn't be too difficult. Just keep shooting at Xedur while you dodge and weave your way through the fight.
Get on the second bubble platform or the solid platform right after that and simply jump over or duck under Telal's projectiles. He alternates between high and low shots, but all of them can be telegraphed by the player. He speeds up as he takes more damage, so be careful near the end of the fight. Those projectiles come flying fast when he turns red. If you fall to the ground, get back on the platform as quickly as possible. Keep shooting right above his head (at the yellow bubbles on his back) and he should go down in no time.
This fight requires more than just a weapon. Your address disruptor also proves useful, so jump up to the second highest purple block and use the disruptor. It will uncover a secret platform. Jump on that one to reach the final purple block at the very top. That purple block is a safe spot, and Uruku can't reach you from there. Wait for your opening to go back and down and shoot at him a few times, then jump back up to the safe spot. Keep repeating this process until all the yellow circles on his head are destroyed, and then aim for the weapons on his belly and his yellow beam arm (the most dangerous part of the fight).
Gir-Tab's only vulnerable spots are his eye (which he often closes) and his belly. The Voranj weapon makes this fight a lot easier, as it hits his belly every now and then with its spread attack. Duck down low and repeatedly shoot the Voranj. Every now and then you'll hit his eye when he opens it or his belly. When Gir-Tab shoots projectiles, jump and duck accordingly. Every now and then Gir-Tab jumps forward and shoots flames, so back up when that happens.
If you don't have the Voranj, use the same strategy and just repeatedly shoot at the eye with the Axiom Disruptor or another long-range weapon. The fight takes longer, but the important part is dodging his projectiles/flames.
Ukhu might be the hardest boss in the game. The hornet-like creature does a ton of damage when it hits the player with its stinger, and we don't want to let that happen. When you move forward, Ukhu moves backwards. Use this to your advantage to create distance. When Ukhu shoots projectiles, avoid them and then retaliate with the Voranj. Try to shoot diagonally, and remember that you can hold L1 to stay in place and shoot in a specific direction.
Ukhu always does his stinger attack after shooting the projectiles, so never move in close after that attack. Eventually Ukhu summons a few smaller enemies and leaves itself vulnerable for a few moments. Get some shots in with the Voranj and then switch to the Kilver to take out the smaller enemies quickly. You can also glitch the small enemies with an address bomb to speed things up. Keep the routine going for the entire fight and always try to avoid that stinger. It may take a few tries, so don't feel too discouraged if you struggle with Ukhu.
Whereas Ukhu is the hardest boss in the game, Sentinel is certainly the most annoying. It constantly spouts out projectiles that seem nearly impossible to avoid. It's all about dealing as much damage as possible in a short amount of time. Basically, kill Sentinel before it kills you. The lightning gun is a good option if you get right under the middle of Sentinel; just be sure to avoid the beam attack as it does a ton of damage. You can actually stay just to the left or right of the beam and still hit Sentinel. Remember to jump every so often to avoid the projectiles, though you'll still get hit frequently. When Sentinel retracts its beam and shoots out a bunch of small white enemies, go in a corner, duck, and hope for the best.
The final boss of the game is surprisingly easy if you know what to do. Get the Kilver or Flamethrower out and continually shoot the three sentinel enemies. Make sure they stay grouped together so they all die at once. They often drop health, so don't worry too much about taking damage. When they're dead, attack the green square in the ceiling, as it's Athetos' weak point. Eventually one of the Rusalki will come over and help. You need to repeat this process three times.
As long as you kill the sentinel enemies quickly enough and all at once, you'll get health back at a constant enough rate to continue the fight and defeat Athetos. Alternately, you can repeatedly dash in the air, which deals damage with the requisite upgrade. It's a little riskier, but it works.