Here is the full list of all 15 Red Death achievements.
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!
I saw something flashing!
That’s a secret! Don't tell anyone!
Arcade Mode unlocked!
...and no one will know!
You better be ready!
Someone to care about!
Now we know!
We'll never know!
It’s a bullet hell afterall!
Finally at level 2!
Meet the first boss.