Here is the full list of all 13 INVITATION To FEAR achievements.
Lose to the puppets.
Destroy a total of 10 cursed statues.
Attacked while holding a frying pan.
Heal your friends with a medikit.
Heal your companions at least 30 times in total.
Clear in single-player mode
Down five times in one game.
Clear with all friends alive.
Your friends are wiped out, and you are the last one left.
Ten times in one game, you will be caught in a surveillance trap.
Invite a friend for the first time.
Invite a friend 15 times.
Invite a friend 50 times.