Here is the full list of all 38 Survive! Mr.Cube trophies - there are 24 bronze, 8 silver, 5 gold and 1 platinum.
Achieved all trophies
Kill the boss
Die 5 times
Find 5 hidden gold chest
Penetrate through 10 stages
Traded with the merchant for 5 times
Traded with the merchant 3 times
Dig a grave of the dead Mr.Cube
Find 3 hidden gold chest
Killed 3 competing CUBE
Destroyed 10 towers
Penetrate through 5 stages
Penetrate through 3 stages
Destroyed 5 towers
Succeeded attacking 10 times with mace
Used the speed enforcement potion 5 times
Used the stamina recovery item 5 times
Find 1 hidden gold chest
Obtained 3 types of equipment
Bought from the merchant for the first time
Succeeded attacking 10 times with spear
Produced new character
Killed 50 monsters
Killed the first competing CUBE
Destroyed the tower for the first time
Used the health recovery item 5 times
Killed 30 monsters
Opened 10 skeleton chest
Obtain 50 gold
Kill the Elite Monster
Opened 5 skeleton chest
Killed 10 monsters
Obtain 25 gold
Succeeded attacking 10 times with sword
Obtain 10 gold
Opened the skeleton chest for the first time
Move to the first stage using the portal
Complete tutorial