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