Pyrogen has 3 attacks, and all can be easily dodged (in terms of dodging Pyrogen himself, which is what matters for his 1-hit kills; avoiding all damage is a little trickier, but doesn't matter if you're just worried about surviving the attacks).
- Bodyslam: Pyrogen will yell "crush!", and charge at Beck. When he gets close, he jumps up and slams down where Beck is standing. To dodge this, dash under Pyrogen (and jump over the flames behind him to avoid other damage).
- Explosion: Pyrogen yells "Here it comes!", charges at Beck, stops in front of him, and yells "Boom!", setting off a large explosion. To dodge this, stand in the middle of the stage (or preferably a bit closer to Pyro's starting side), facing away from Pyro, and dash away quickly once he is close enough to stop. If you don't move at all, he may or may not grab you for the insta-kill (explosion WILL hurt).
- Charge: Pyrogen does not yell anything, and simply charges across the stage, leaving fire behind him. To dodge, just jump over him and dash over the fire behind him (watch out for the fire on the far wall). For an easier time, use Avi's weapon if you have it to jump higher.
The reason the first round of insta-kill attacks is so hard to avoid is because the annoying dialog that shows up mid-fight blocks Pyrogen's audio clues. He does also have physical/visual cues for which attack is coming, so if you can keep an eye on that, you can dodge the first round (audio comes back later in the fight).
Additional tip: once you absorb him once, his 1-hit kill power will go away until the next time he recharges in the foreground, so you want to get his health down quickly to reduce his insta-kill opportunity. If you have Avi's weapon, it's a good way to chip his health down quickly (although you have to get pretty close to make sure it hits).