Here is the full list of all 51 Streets of Rogue trophies - there are 44 bronze, 4 silver, 2 gold and 1 platinum.
Unlock playable character
Unlock elevator access
Complete Industrial
Have four status effects at once
Kill everyone in a level
Complete Slums
Complete Any Floor
Complete Tutorial
Complete All Trophies
Complete Park
Complete Downtown
Complete Uptown
Kill the Killer Robot
Find the Alien
Make a Refrigerator "Run"
Kill a Vampire while playing a Werewolf
Fall off the edge of the map
Create a custom character
Poison a water body with Resurrection Shampoo
Enslave a Slavemaster
Win an Arena fight
Nicely ask an NPC to leave a level
Electrocute someone in water
Kill someone by throwing a Gravestone at them
Give someone a Cyanide Cocktail
Complete Mayor Village
Win Election
Neutralize Mayor
Win without winning election or neutralizing Mayor
Find the Bad Ending
Complete any Big Quest