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