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