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
Die 5 times
Penetrate through 10 stages
Killed 3 competing CUBE
Find 5 hidden gold chest
Destroyed 10 towers
Traded with the merchant for 5 times
Kill the boss
Killed the first competing CUBE
Penetrate through 5 stages
Find 3 hidden gold chest
Succeeded attacking 10 times with mace
Obtained 3 types of equipment
Traded with the merchant 3 times
Destroyed 5 towers
Succeeded attacking 10 times with spear
Dig a grave of the dead Mr.Cube
Bought from the merchant for the first time
Produced new character
Find 1 hidden gold chest
Used the speed enforcement potion 5 times
Used the health recovery item 5 times
Killed 50 monsters
Penetrate through 3 stages
Opened 10 skeleton chest
Killed 30 monsters
Used the stamina recovery item 5 times
Obtain 50 gold
Opened 5 skeleton chest
Killed 10 monsters
Obtain 25 gold
Obtain 10 gold
Destroyed the tower for the first time
Kill the Elite Monster
Succeeded attacking 10 times with sword
Opened the skeleton chest for the first time
Move to the first stage using the portal
Complete tutorial