Here is the full list of all 21 Vesta achievements.
Finish the game.
Find all secrets.
Complete the third chapter
Activate 20 checkpoints.
Destroy 5 Punchers.
Destroy 10 MinePlanters.
Complete the second chapter.
Find 50 secrets.
Destroy 50 enemies.
Find 25 secretos.
Destroy 25 enemies.
Use 50 energy drums.
Destroy 10 patrollers.
Complete the first chapter.
Shoot 50 times.
Destroy 30 crates.
Use 25 energy drums.
Read 5 consoles.
Destroy 5 enemies.
Find 5 secrets.
Use 5 energy drums.