Here is the full list of all 13 Ion Assault HD trophies - there are 9 bronze, 3 silver and 1 gold.
Complete the cooperative campaign.
Score exceeds 5,000,000 points (Campaign).
Complete a whole sector without dying once.
Score exceeds 2,500,000 points (Survival).
Complete the single player campaign.
Score 1,500,000 points in a single game.
Collect enough Score Orbs in a single run to get two extra lives at once.
Destroy five asteroids at once.
Finish a stage in less than 60 seconds.
Destroy 50 big obstacles in a single game.
Survive 3 stages without dying once.
Complete a stage without collecting a Power-Up.
Score exceeds 1,000,000 points (Survival).