Here is the full list of all 51 Persona 4 Arena Ultimax achievements.
You completed Arcade Mode with one character.
Failed a Reversal Burst in Arcade or Network Modes.
You performed 100 Furious Actions in the Arcade or Network Modes.
Your opponent failed a Reversal Burst in the Arcade or Network Modes.
You completed 20 Network matches.
You pulled off 100 Auto Combos in the Arcade or Network Modes.
You used an Awakened SP Skill Boost in Arcade or Network Modes.
You performed 10 Fatal Counters in Arcade or Network Modes.
You won your first Network match!
You studied 20 different Lessons.
You started on the road to knowledge.
You started an episode in Story Mode.
You mastered Persona 4 Arena Ultimax!
You completed Arcade Mode with three characters.
You completed one Score Attack course.
You completed three Score Attack courses!
You completed five Score Attack courses!
You completed Story Mode from the P4 perspective.
You completed Story Mode from the P3 perspective.
You witnessed the story's True Ending.
You raised a character to level 10 in Golden Arena Mode!
You raised a character to level 30 in Golden Arena Mode!
You raised a character to level 50 in Golden Arena Mode!
You defeated a boss character in Golden Arena Mode!
You completed one Golden Arena course.
You completed two Golden Arena courses.
You completed three Golden Arena courses.
You maxed out a Social Link in Golden Arena Mode!
You trained for 30 minutes straight!
You completed all of one character's challenges!
You completed 150 challenges!
You completed 300 challenges!
You reached Level 30 in Network Mode.
You did battle against all the different characters in the Network Mode.
You defeated all the Shadow characters playing in the Network Mode.
You fought your own Shadow in Network Mode!
You completed 50 Network matches.
You completed 100 Network matches.
You used all the characters in Network Mode!
You reached Grade F.
You reached Grade E+.
You reached Grade C.
You watched a replay in the Theater. Was it everything you dreamed of?
You've registered a Rival in the Player List.
Hit a home run with the bases loaded, full count and two outs in the Arcade or Network Modes.
You used the S Hold System 10 times in Arcade Mode.
You won 30 rounds with SP Skills or Awakened SP Skills in Arcade or Network Modes.
You went on a Shadow Frenzy!
You defeated an opponent without letting them Awaken in Arcade or Network Modes.
You successfully used each character's Instant Kill move in Arcade or Network Modes.
You achieved a Perfect victory in Arcade or Network Modes!