Here is the full list of all 15 Red Death achievements.
I saw something flashing!
That’s a secret! Don't tell anyone!
survive 10 rounds in arcade mode
survive 7 rounds in arcade mode!
survive 5 rounds in arcade mode!
Die 5 times without closing the game!
Arcade Mode unlocked!
...and no one will know!
You better be ready!
Someone to care about!
Now we know!
We'll never know!
Finally at level 2!
It’s a bullet hell afterall!
Meet the first boss.