Here is the full list of all 34 Chocobo's Mystery Dungeon EVERY BUDDY! trophies - there are 16 bronze, 12 silver, 5 gold and 1 platinum.
Increased your gear's level to +99.
Defeated Shinryu.
Used every type of magicite.
Collected one of every type of collar.
Fused an ALL brand.
Completed Chapter V.
Reached Floor 100 of the Insatiable Hunger dungeon.
Befriended a boss monster.
Maxed out one job.
Raised Chocobo to Level 50.
Defeated 6 monsters with a single attack by Chocobo.
Completed Chapter IV.
Befriended 60 monsters or characters.
Completed Chapter III.
Completed Chapter II.
Befriended 20 monsters or characters.
Completed Chapter I.
Completed the tutorial.
Collected all trophies.
Collected one pair of every type of talons.
Collected one of every type of saddle.
Collected one of every type of item.
Completed a dungeon with every type of monster as a buddy.
Befriended all monsters and characters.
Completed all Dungeons of Remembrance.
Completed all dungeons.
Reached Floor 500 of the Insatiable Hunger dungeon.
Completed a 20-floor dungeon without triggering a trap.
Defeated 10 monsters with a single attack by Chocobo.
Defeated Omega.
Maxed out Chocobo's level.
Acquired all jobs.
Completed a dungeon with every job.
Maxed out all jobs.