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