Here is the full list of all 15 Score Rush Extended trophies - there are 13 bronze, 1 silver and 1 gold.
Kill enemy with collision.
Move with slowdown for 1 minute.
Survive 5 minutes without launching nuke.
Collect a 1UP.
Kill a boss in under 10 seconds.
Shoot 500,000 bullets in a single game.
Max out main gun firepower.
Have 3 fighters in reserve (collect a 1UP without dying) in SINGLE PLAYER + SOLO PLAY mode.
Survive 1 minute without shooting.
Coalesce 50% of trailing options (collect 16).
Kill boss for 20 million points.
Max out trailing options (collect 32).
Witness 1,000 enemy bullets at once.
Beat BOSS RUSH in any difficulty.
Beat SCORE RUSH in any difficulty.