Here is the full list of all 20 Dead Dust (JP) trophies - there are 11 silver, 8 gold and 1 platinum.
Platinum trophy
Shoot 777 times
Kill an enemy with tomahawk
Kill an enemy with dynamite
Kill 50 enemies
Kill 100 enemies
Kill 150 enemies
Complete the first level
Kill the chieftan
Complete 3 levels
Complete 6 levels
Earn 1$ in savings
Make a first purchase at saloon
Collect a medkit
Collect 3 medkits
Open a box
Open 5 boxes
Complete the "train level"
Complete the "horse level"
Complete the game