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