Here is the full list of all 46 The King of Fighters XIII Steam Edition achievements.
Perform 50 Super Special Moves Finishes (Arcade, Versus)
Play 50 [ranked matches / player matches]
Win 5 [ranked matches / player matches]
Create 10 rooms
Perform 300 Target Actions (Arcade)
Clear STORY.
Register an icon, team and message in Customize
Win your first [ranked match / player match]
Be challenged by "Ash" and win in ARCADE
Play your first [ranked match / player match]
Perform 10 Perfect Victories (Arcade, Versus)
Create 10 characters in Customize
Hit 100 times using Super Special Moves (Arcade, Versus)
Be challenged by "Saiki" and win in ARCADE
Get 10 straight wins (Arcade, Versus)
Defeat 3 characters in Survival mode
Hit 100 times using Special Moves (Arcade, Versus)
Get an SS at the victory screen
Be challenged by "Billy" and win in ARCADE
Perform 10 Target Actions (Arcade)
Get an S at the victory screen
Complete STORY.
Hit 100 times using EX Special Moves (Arcade, Versus)
Hit 100 times using EX Super Special Moves (Arcade, Versus)
Hit 100 times using NEO MAX Super Special Moves (Arcade, Versus)
Get 50 NEO MAX Super Special Moves Finishes (Arcade, Versus)
Perform 50 Drive Cancels (Arcade, Versus)
Perform 50 Super Cancels (Arcade, Versus)
Perform 50 HD Cancels (Arcade, Versus)
Perform 50 MAX Cancels (Arcade, Versus)
Complete the tutorial
Clear ARCADE MODE without continuing
Clear ARCADE MODE on VERY HARD
Clear Time Attack mode for the first time
Clear Time Attack mode with 30 characters
Defeat 35 characters in Survival mode
Complete all trials for 1 character in Trial mode
Clear 200 trials in Trial mode
Play 100 [ranked matches / player matches]
Play 300 [ranked matches / player matches]
Win 25 [ranked matches / player matches]
Win 50 [ranked matches / player matches]
Win 100 [ranked matches / player matches]
Get 2 consecutive wins in a ranked match
Get 5 consecutive wins in a ranked match
Get 10 consecutive wins in a ranked match