Here is the full list of all 15 DOOM VFR achievements.
Fully upgrade a single Combat Chassis subsystem
Telefrag into 25 demons
Complete the first laser minigame
Put out the fires in the BFG central chamber
Complete the first level
Use a Weapon Upgrade Station
Use an Argent Cache
Shoot down 30 projectiles
Teleport 1000 times
Telefrag into a Possessed Engineer and explode
Complete all of the hacking minigames
Acquire all weapons
Travel to Hell
Collect all of the DoomGuy Dolls
Complete the single player campaign on any difficulty