Ok first of have you fed your chocobo as much greens as possible?, secondly what kind of chocobo is it? if its a poor one then its stats wont go very high, better chocobos=better stats asnd can be maxed higher, really poor nes can only really reach 70-80 speed.

Also do you use the refil stamina "cheat" , press L1, L2, R1, and R2 while using the boost to slow it going down and if your going along normaly it refils stamina fairly quick