Here is the full list of all 40 Rush to Adventure achievements.
You have slayed a lot of monsters
Play through all towers
3 hours total combined playtime
Kill the grey golem
You will not give up
Collect 500 coins
2 hours total combined playtime
Kill the blue golem
You are being noticed
Collect 300
You can handle this
Unlock all abilities
1 hour total combined playtime
Collect 200 coins
Kill the red golem
You had a look around
Kill the green golem
Collect 100 coins
You are still unknown
You just woke up
Collect all weapons
Beat all levels
Complete the game
Find all the gems
Find it
Get 100%!
Beat the game on hard or better
Beat the game on insane
Beat the game without dying
Beat the game under 90 minutes
Get minimum rank C on everything
Get minimum rank B on everything
Get minimum rank A on everything
Get rank S on everything
5 hours total combined playtime
You will destroy this evil
You are a living legend
You are untuchable
You have been found worthy
Beat the game under 60 minutes