Originally Posted by The MaDaBa
First of all, it's best to stay with Modern Sonic at all times with one exception late in the fight.
I found slipping to Classic Sonic more often helped keep my ring count healthier, I know I was more open to the Homing attack there but it was the risk I was willing to take.
I only did this while the Time Eater was also in the 2D plane so I wasn't wasting valuable time catching up to him in the 3D plane.
Another valuable time for ring collecting is after the 1st and 2nd time you've hit the core because the Time Eater will only slip into the 2D plane anyway after a short period of time.
This was just my way of doing it. This achievement is frustrating but it's one of those that you get better at each time I think.