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