Well I got my Chocobo companion to Rank-4 today. The only way that I found to make it level is by chaining mobs which were +1/+2/+3 in level to me. I can usually get chain #5 during the farming. Your Chocobo companion doesn't appear to get XP from Fates or Quest turn ins. The design behind the whole Chocobo companion would be perfect if there were no Fates in the game. No one will be grinding their way to multiple 50s by justing farming mobs.