This Seeking Tech guide will explain how you can beat Mighty Chewy without taking any damage. Use the following video as a reference:
For the first phase, you need to make your way to the main arena. To do so, you will have to jump from one platform to another while defeating enemies along the way.
When you land on the buildings, avoid staying close to the north side to dodge the beam attacks. Otherwise, you should take your time, especially against the spike and electric enemies.
Once you get to the arena, take care of the first wave of enemies. Afterwards, Chewy will send a blockade towards you. Position yourself in the middle and then use your boost power-up to smash through the glass panels. Try not to go too early as you may end up boosting off of the building
During the Bell attack, avoid the shockwave and then use your boost to attack the bell. You can then hit chewy in the eye.
Next, you need to boost through more barriers. You will need to pick the left or right panel for the first one. Afterwards, you need to jump up the beam and then jump again to boost through the second one.
You then need to take care of the second wave of enemies and then focus on the second bell. Take it out and then attack the other eye
When chewy splits the building apart you need to jump and hover over to the other side.
The boss will then bite down on the arena, causing a shockwave. Try to stay in the middle to give yourself a bit of time to plan your jumps. Once you survive the shock waves, move in to attack his teeth. Repeat this process to get rid of his other teeth.
Once his mouth is opened, use the boost on the target to finish the fight.