Here is the full list of all 13 Past Cure trophies - there are 9 bronze, 3 silver and 1 gold.
Escape the prison dead or alive.
Get the contents of Dr. Fletcher's suitcase and unlock every safe.
Make your way up to the lobby.
Kill an agent that sees you before he can call for help.
Clear the level "Past Secrets."
Clear the level "Sleepless Nights."
Clear the level "My Peronal Battlefield."
Retrieve the black pill.
Take the black pill and defeat Amos.
Kill 5 agents in a row while in slow motion.
Kill 25 porcelain figures in your nightmare.
Perform 3 full combos that kill enemies within 10 seconds.
Kill 3 agents with one shot.