One way is through a self - sacrifice on Raph's part. If Raph hurt Mikey because of some external factor like being controlled, he could put himself in harm's way to save Mikey from a greater danger later. This act of redemption would make Mikey forgive him and they could end up with a stronger bond. The other turtles could also play a role in facilitating their reconciliation by showing support and understanding for both of them.
The story could end on a positive note if Raph sincerely apologizes to Mikey. He can admit his mistake, whether it was due to anger, misunderstanding or accident. Mikey, being the kind - hearted turtle he is, forgives Raph. Then they have a moment of brotherly bonding, like sharing a pizza or just hanging out together, showing that their relationship is mended.
A positive ending could come from Raph and Mikey learning from the experience. They could start a new training regime together where Raph learns better control and Mikey learns to be more aware of his surroundings. This growth and cooperation between them would not only heal the rift but also improve their skills. They could then go on to face a new enemy as a united front, with their brotherly love and trust restored.