Here is the full list of all 13 INVITATION To FEAR achievements.
Invite a friend 50 times.
Invite a friend 15 times.
Down five times in one game.
Your friends are wiped out, and you are the last one left.
Destroy a total of 10 cursed statues.
Ten times in one game, you will be caught in a surveillance trap.
Lose to the puppets.
Invite a friend for the first time.
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
Clear with all friends alive.