Here is the full list of all 13 Past Cure achievements.
Kill an agent that saw you before he can call for help
Finish the nightmare level
Finish the designhouse level
Complete the chessroom level
Make your way through the parklinglot
Get the contents of the suitcase of Dr. Fletcher
Survive the prison
Defend Sophia's apartment
Defeat Amos
Kill 5 Agents in a row while in slomo
Kill 25 porcelainfigures in your nightmare
Complete 3 full combo's killing your enemy's within 10 seconds
Kill 3 Agents in one shot