Here is the full list of all 13 Deadstorm Pirates trophies - there are 9 bronze, 3 silver and 1 gold.
Clear all stages in Arcade Mode from Stormy Sea onward without continues.
Obtain an S Rank in all stages.
Clear all stages in Ranking Mode from Stormy Sea onward.
Obtain a "Nice Combination!" rating 100 times.
Clear the Stormy Sea in Arcade.
Clear the Mountain Stream.
Clear the Cave in Arcade.
Clear the Great Whirlpool in Arcade.
Clear the Treasure in Arcade.
Register a score in Ranking Mode.
Reach a Teamwork Level of 100%.
Reach a total of 10000 kills.
Obtain a YO-HO-HO rating while manning the helm.