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