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