I'm going to keep this guide quick and easy for you to read. When unlocking this achievement it doesn't matter if you hit the debris as it doesn't count as taking damage. A quick thing to note when fighting time eater is to get as much damage as you can when the opportunity presents itself, mostly so you can stop having anxiety over taking damage then having to restart all over again.

Some guidance on how to avoid most attacks. when the time eater is charging its laser make sure to switch to classic or modern sonic depending on where the time eater is, This is probably the only annoying attack that can crush your no hit run completely, plus you can gain the ground you lost pretty easily. Homing shots can be tricky to deal with, however can be easily avoided by luring them to one corner of the screen. The attack that slows down time can only be avoided if you attack the boss as its charging up.

I know this was a short guide but I hope this can come in handy for those trying to 100% complete this game!