Sonic Generations - Time Eater Single Segment Strat Tutorial

So, in order the beat Time Eater you're required to hit him 3 times. With the method I will show here, you should be able to beat him with the time of 1:12-1:15.

For the first hit, all you need to do is to boost and try to avoid getting hit. There is a possibilty of avoiding Time Eater's attack before you can hit him, but that's not very consistent so I decided not to use it here.

After completing the first hit, you want to switch to Classic, and then wait for the moment your screen is flashing. At this moment, you want to switch back to Modern. Doing that will lead to to out of bounds. You should boost when you're out of bounds for about 2 seconds and then press Y twice quickly. That would lead you really close to Time Eater and you'll be able to get the second hit easily. (This strat was found by theultimategamer95)

After completing the secend hit, you should start mashing Y as fast as you can and keep boosting this whole time. To avoid timing issues, you might want to start mashing Y during the animation of the secend hit. You want to keep mashing Y button until you see Time Eater's eyes open (about 00:45 in video time). When you see that his eyes are open, stop mashing. If you stopped mashing and you're in Classic Sonic, quickly switch to Modern again and boost towards the boss. If you stopped mashing and you're in Modern Sonic, just keep boosting towards the boss.
Assuming your timing and mashes were good enough, you should be able to boost until you're close enough to the boss, so he will try to attack you. You want to avoid getting any damage during this time and after his attack you can get the third hit.

Gameped viewer is shown at down-right side of the screen to help you see what inputs you should do it real time.
Good luck and enjoy!