Here is the full list of all 29 Phantom Brave PC achievements.
Completed Part 1
Obtained 20 job classes
Completed a Random Dungeon
Take 10 items home to Phantom Isle
Got control of Phantom Isle
Completed Part 2
Completed Part 3
Completed Part 4
Completed the Another Marona extra scenario
Defeated the 5 heroes in the Hermuda Triangle
Defeated Laharl in Extra Map 1: "????"
Defeated Etna and Flonne in Extra Map 2: "Throne Room"
Defeated Laharl, Etna, and Flonne in Extra Map 3: "Throne Room"
Defeated Laharl in Extra Map 4: "Throne Room"
Defeated Mid-Boss (Vyers) in Extra Map 5: "Throne Room"
Defeated Sienna in Extra Map 6: "????"
Defeated Sulphur in Extra Map 7: "????"
Defeated Myao in Extra Map 8: "????"
Defeated Baal in Extra Map 9: "New Challenger!"
Defeated Pringer X in Extra Map 10: "New Challenger!"
Defeated Pringer XX in Extra Map 11: "New Challenger! Cont."
Defeated Pringer XXX in Extra Map 12: "New Challenger! More"
Made 20 phantoms at Phantom Isle
Obtained all job classes
Reached LV 9999 with Marona, a phantom, or an item
Obtained a Rank 7 title
Reincarnated a spiritless character
Obtained the hidden bordeaux, changebook, and Bottle Mail on Phantom Isle
Unlocked all achievements!