Here are all of the achievements unlocked in Game Center. Achievements for Clearing an episode bring 10 points, achievements for episode specific actions bring 20 points and achievements for overall actions bring 30 points. Completing the game gets you 50 points.

Achievement	How to unlock
"Le francais" de Jean	Learn all of the "French" Jean Armstrong has to impart, Ep. 3 of PW AA " T&T
"Rookie Killer" Killer	Clear the 1st episode of all three games
Ace Attorney	Clear all of PW AA Trilogy HD
Beware, Your Honor!	Press Dahlia when she claims "The truth is... Feenie pushed him twice.", Ep. 1 of PW AA " T&T
Bridge to Turnabout	Cleared Ep. 5 of PW AA " T&T
Bug Sweeper	Find a bug with a bug sweeper
Cordyline Stricta	Examine the office plant while Gumshoe is at the Fey & Co. Law Offices, Ep. 2 of PW AA
Dabbling in Fingerprints	Complete a fingerprint analysis
Edgeworth's Grand Debut	See every animation young Edgeworth has to offer, Ep. 4 of PW AA " T&T
Farewell, My Turnabout	Cleared Ep. 4 of PW AA " JFA
First Steps	Started playing PW AA Trilogy HD
Hardcore Steel Samurai Fan	Clear all of "Turnabout Samurai" and "Farewell, My Turnabout"
His Name is... Charley?	Examine the office plant while Maya is channeling Mia, Ep. 3 of PW AA
I Hate Childhood Friends	Present Phoenix' Attorney's Badge to Larry and examine the string of flags, Ep. 5 of PW AA " T&T
Illuminating Luminol	Find blood with Luminol
Innocent Engarde...?	Plead that Matt Engarde is not guilty, Ep. 4 of PW AA " JFA
I'm an Investigative Photographer	Press "I'm an investigative photographer." during "Lotta's New Testimony", Ep. 4 of PW AA
Judge Wackner	Press Oldbag when she claims "It was the Nickel Samurai that I saw!", Ep. 4 of PW AA " JFA
Justice Ill Served	Get a bad ending
Justified Self-Defense	Plead that it was justified self-defense, Ep. 2 of PW AA " JFA
Ladders vs. Step-Ladders	Get every ladder vs step-ladder conversation
Lunchbox Specialist	Lunchbox Specialist (Check out every lunchbox Angel Starr has to offer
Master of Kurain	Clear all of PW AA Ep. 2, PW AA " JFA Ep. 2, PW AA " T&T Eps. 2 and 5
Metal Detector	Find something with a metal detector
Mind Your Own Business, Pal!	Press Gumshoe about "It sounded like they were even talking about marriage.", Ep. 1 of PW AA " JFA
Naruhodo A. Wrighto	Present Maya with Max' profile in Phoenix' office after taking his case, Ep. 3 of PW AA " JFA
Not So Mysterious After All	Try to move before hearing everything Iris has to say in the Main Hall, Ep. 5 of PW AA " T&T
On Billy's Head!?	Spray Luminol on the guard station cactus' head, Ep. 5 of PW AA
Please Turn In Your Badge	Answered "Mia Fey" when the Judge asked who the victim was, Ep. 1 of PW AA
Psyche-Unlock	Break a Psyche-Lock
Recipe for Turnabout	Cleared Ep. 3 of PW AA " T&T
Reunion, and Turnabout	Cleared Ep. 2 of PW AA " JFA
Rise from the Ashes	Cleared Ep. 5 of PW AA
Secret Weapons Three	Borrow all 3 of Gumshoe's secret weapons, Ep. 4 of PW AA
Smells Like Oldbag	Examine the alien wear in Mask*DeMasque's Hideout & Oldbag's Command Vest at KB Security, Ep. 2 of PW AA " T&T
The Back of My Badge	Examine the back of Phoenix' Attorney's Badge, Ep. 5 of PW AA
The First Turnabout	Cleared Ep. 1 of PW AA
The Lost Turnabout	Cleared Ep. 1 of PW AA " JFA
The Stolen Turnabout	Cleared Ep. 2 of PW AA " T&T
The Whole Truth	Present the Victim's Note during the 1st cross-examination, Ep. 4 of PW AA " T&T
Turnabout Beginnings	Cleared Ep. 4 of PW AA " T&T
Turnabout Big Top	Cleared Ep. 3 of PW AA " JFA
Turnabout Goodbyes	Cleared Ep. 4 of PW AA
Turnabout Memories	Cleared Ep. 1 of PW AA " T&T
Turnabout Samurai	Cleared Ep. 3 of PW AA
Turnabout Sisters	Cleared Ep. 2 of PW AA
Um, Lotta Hair, Was It?	Say that Lotta's full name is Lotta Hair in the Winding Way, Ep. 2 of PW AA " JFA
Violetta's Home-Made Donuts	Have a donut offered to Phoenix by Viola, Ep. 3 of PW AA " T&T
What's Important Here?	Assert that the name on the card is what's important, Ep. 1 of PW AA " JFA
Wrath of a Judge	Assert that the murder weapon is under the Judge's bench, Ep. 3 of PW AA " JFA