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.
Completed Chapter I.
Completed the tutorial.
Collected all trophies.
Completed Chapter II.
Completed Chapter III.
Completed Chapter IV.
Completed Chapter V.
Collected one of every type of collar.
Collected one pair of every type of talons.
Collected one of every type of saddle.
Collected one of every type of item.
Befriended 20 monsters or characters.
Befriended a boss monster.
Befriended 60 monsters or characters.
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 100 of the Insatiable Hunger dungeon.
Reached Floor 500 of the Insatiable Hunger dungeon.
Increased your gear's level to +99.
Fused an ALL brand.
Used every type of magicite.
Completed a 20-floor dungeon without triggering a trap.
Defeated 6 monsters with a single attack by Chocobo.
Defeated 10 monsters with a single attack by Chocobo.
Defeated Shinryu.
Defeated Omega.
Raised Chocobo to Level 50.
Maxed out Chocobo's level.
Acquired all jobs.
Maxed out one job.
Completed a dungeon with every job.
Maxed out all jobs.