When a lethal alien is brought on board a spaceship by accident, the crew has to fight for their survival in order to escape

maybe

When a lethal alien is brought on board a spaceship, the small crew must to fight to the last man to avoid taking the monster back to earth.

ALIEN$

I agree with the previous penpusher. The beginning could also be something in the lines of "When accidentally bringing a lethal alien onboard the spaceship..."

Nice work, I need to rewatch this one. Maybe change out "the crew" to the main character?