Here is the full list of all 36 Vector Strain achievements.
Complete STAGE 3 on "Beginner" difficulty
Complete STAGE 3 on "Standard" difficulty
Complete STAGE 2 on "Standard" difficulty
Get a 10 000 000 score
Complete STAGE 1 on "Standard" difficulty
"Complete STAGE 2 on "Beginner" difficulty
Get a 5 000 000 score
Complete STAGE 1 on "Beginner" difficulty
Complete STAGE 1 on "Hardcore" difficulty
Complete STAGE 2 on "Hardcore" difficulty
Complete STAGE 3 on "Hardcore" difficulty
Complete STAGE 4 on "Beginner" difficulty
Complete STAGE 4 on "Standard" difficulty
Complete STAGE 4 on "Hardcore" difficulty
Complete STAGE 5 on "Beginner" difficulty
Complete STAGE 5 on "Standard" difficulty
Complete STAGE 5 on "Hardcore" difficulty
Finish the game without using any continues on "Beginner" difficulty
Finish the game without using any continues on "Standard" difficulty
Finish the game without using any continues on "Hardcore" difficulty
Gather 50 stars
Gather 100 stars
Gather 200 Stars
Get a 20 000 000 score
Get a 50 000 000 score
Get a 100 000 000 score
Unlock the "Avatar" ship by finishing the game without using any continues on any difficulty
Unlock the "Oblivion" ship by collecting 120 stars
Complete any stage without using the shield
Complete all stages with a 5 star rating
Beat the game without loosing any ship
Complete the game with the "Vector" ship
Complete the game with the "Predator" ship
Complete the game with the "Raptor" ship
Complete the game with the "Avatar" ship
Complete the game with the "Oblivion" ship