Here is the full list of all 25 Cutthroat achievements.
Try all characters
Try all maps
Try all game modes
Complete Missions 1 and 2
Complete Mission 2 (Hard) solo
Complete all missions
Win an online match
Enter Sudden Death
Spend 1:30 in Sudden Death
End a match with all players dead
Get 1 kill
Get 50 kills
Get 250 kills
Get 500 kills
Kill 1 innocent
Kill 100 innocents
Kill 500 innocents
Kill 1000 innocents
Create a local profile
Create 4 local profiles
Create 10 local profiles
Win a perfect match as a Rogue. This means a score of 3-0 with only delayed kills (no auto attacks)
Use Soul Swap to avoid death
Kill a marked target as a Ranger
Get a kill in the first 2 seconds using Riot