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