Here is the full list of all 36 Persona 3 Portable achievements. It takes around 80-100 hours to unlock all of the achievements on Windows.
Defeat Nyx.
Defeat Nyx Avatar.
Defeat Elizabeth or Theodore.
Defeat Margaret.
Defeat The Reaper.
Perform 50 Persona fusions.
Max out 10 Social Links.
Defeat the Hanged Man.
Register over 50% of the Compendium.
Switch Personas 5 times in 1 battle.
Max out all social qualities.
Defeat the Fortune and Strength.
Enter a special relationship with someone.
Deal over 999 damage in 1 attack.
Use 4 or more Personas in a special fusion.
Defeat the Hermit.
Max out a Social Link.
Defeat the Chariot and Justice.
Rank #1 in your class on an exam.
Defeat the Hierophant and Lovers.
Rescue a missing person.
Defeat the Emperor and Empress.
Summon a Persona from the Compendium.
Perform 50 All-Out Attacks.
Buy 5 things from Tanaka's Amazing Commodities.
Defeat the Priestess.
Fight a battle in costume.
Exploit enemy weaknesses 100 times.
Defeat a Golden Hand.
Enter a battle with Player Advantage.
Awaken as a Persona-user.
Earn all achievements.
Complete the Persona Compendium.
Max out all social links.
Beat the game with each protagonist.
Experience a fusion accident.