Here is the full list of all 23 Serious Sam 3 VR: BFE achievements.
Blow a Major Biomechanoid into pieces.
Solve the riddle of the Sphynx.
Defeat the spaceship.
Secure the bird.
Find at least 10 secrets in single player.
Rescue professor Stein. So to say.
Complete any level in single player.
Decipher an Egyptian text.
Find Sam's classic outfit
Kill at least 5 headless kamikazes in one explosion.
Complete any level in cooperative with at least 2 players.
Kill an enemy using the Mutilator.
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.
Awake the Guardian of Time.
Kill 5 Cave Demons while they're in air.
Gib 20 enemies from close range with a shotgun.
Use the Mutilator to surf after a Werebull.
Complete the game in single player on unmodified serious difficulty.
Complete the game in single player in the estimated time on each level.