A soldier in rank for The Warriors, Cochise shows his fighting skills on multiple occasions during the film. His ability is on display when he's brawling with The Punks. However, he almost his end when he's lured into a trap by The Lizzies. Falling for the charms of these tough sisters was almost a fatal mistake for Cochise. Luckily for him, Rembrandt was wise to it and The Lizzies were pretty inept at taking advantage of their positions of power.
Cochise is one of The Warriors that makes it home safely to Coney Island in the film. In the video game, his story doesn't progress much further than that. His character and backstory are fleshed out though.
We learn that he earned those feather earrings he's wearing, conquering formidable foes like Big Moe. In Jailbreak, we see Cochise lead a section of The Warriors and emerge unscathed.