Here is the full list of all 21 Rusty Gun trophies - there are 2 bronze, 10 silver, 8 gold and 1 platinum.
Obtain all trophies
Kill your first enemy
Collect 50 bottles
Find a calendar
Complete first level
Kill 30 enemies
Complete the car level
Kill the first boss
Perform 50 slides
Kill 72 enemies
Kill 150 enemies
Kill the second boss
Complete the level on skateboard
Kill the third boss
Don't talk, just crouch till you drop. 44 times, to be exact
Complete the level on boat
Kill the fourth boss
Jump 200 times
Die 15 times
Blow up on three mines
Complete the game