Unmissable story achievement - this is in
STAGE 9My 'non-spoiler' tip would be: keep up with him, whilst dodging obstacles.
I feel most people should know what to do at this point in the game, even if it takes a couple tries, but if you are still struggling:
*** Spoiler - click to reveal ***The battle is on a giant snake, and you will be running along and revolving around it whilst trying to use the air attack on Infinite. He kind of follows you and fires missiles that are easy to dodge without trying really, and so the challenge is in dodging the red 'glitchy' obstacles that run around the snake, whilst also kind of keeping track of him.
The battle always seems to start with the obstacles in the same layout - 3 rings around the snake that you'll have to jump over, then a long one that rotates around the snake that you rotate round with (you can jump this as well but I'd suggest just moving with it). Once you get near enough to Infinite, the air attack icon appears on him, so use it to do a bit of damage. This seems to reset the obstacles, and also has a chance of spawning big spike balls that rotate around the snake that you'll have to dodge also. You can't jump these as they are too big.
If you get hit by an obstacle, you obviously lose a few coins, but it seems Infinite gets a bit further away, and so it takes longer to catch up to him.
You will probably get to the end of the snake a few times, but sonic just does an animation to bounce to the start of the snake again. In my experience, it didn't put me straight in front of an obstacle when this happened, but be wary the obstacles may have changed as I mentioned.
Finally, a couple times in the fight, Infinite will duplicate himself and fly in almost a diamond formation. Simply spam A to air dash attack, as he will be the last one at the back. I believe the second time this happens will always be the final blow of the fight.