Here is the full list of all 23 Serious Sam 3 VR: BFE achievements.
Complete any level in cooperative with at least 2 players.
Rescue professor Stein. So to say.
Complete any level in single player.
Kill at least 5 headless kamikazes in one explosion.
Secure the bird.
Decipher an Egyptian text.
Defeat the spaceship.
Kill an enemy using the Mutilator.
Solve the riddle of the Sphynx.
Kill a Witch-Bride of Achriman.
Smash 20 Kleers with the Sledgehammer.
Power up the Timelock.
Kill 20 enemies with the Minigun without releasing the trigger.
Start the car.
Find Sam's classic outfit
Awake the Guardian of Time.
Kill 5 Cave Demons while they're in air.
Gib 20 enemies from close range with a shotgun.
Blow a Major Biomechanoid into pieces.
Use the Mutilator to surf after a Werebull.
Find at least 10 secrets in single player.
Complete the game in single player on unmodified serious difficulty.
Complete the game in single player in the estimated time on each level.