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