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