Here is the full list of all 14 Smash 'N' Survive trophies - there are 11 bronze, 2 silver and 1 gold.
Barely survive the 'Respect' Mission
Complete the campaign mode
Successfully plant and explode a bomb in Campaign Mode.
Successfully chase and destroy an escaping enemy
Successfully defend your base against an enemy attempt to plant and explode a bomb in Campaign Mode.
Successfully diffuse a planted bomb in Campaign Mode.
Successfully escort an ally to safety
After winning a team derby match
Kill an ally by mistake or on purpose
Complete the trail mission to Join the Necromancers
Do a successful jump from one ship to another
Win 'Respect' mission
Get your First Kill
Entered shop for the first time.