In order to unlock the "Ultra" Difficulty, you need to find a few clues in the base game mode.

The first clue spawns right before you enter the Mom Boss or right after you defeated her.

Hint text for clue 2:
"Well done my friend!
You found the first clue...
To find clue number two
you need to play prison guard!
Watch peacefully over your inmates for 30 seconds
in a room often locked behind iron bars."

The second clue requires you to be inside a challenge room, without killing an enemy for 30 seconds while in there. every few seconds, new fly enemies will spawn while the timer runs down.

Hint text for clue 3:
"You found clue number two!
Congratulations!
Clue number three can only be found...
when you are followed by a devilish airborn beeing,
and anger a busy salesman."

The third clue requires you to destroy the shop keeper with a bomb or another method, while having a devil themed Familiar.

Hint text for clue 4:
"Clue three was quite easy right?
But what horrible thing you did to find it...
To redeem yourself...
Your next task is to clean up a bit.
Destroy 50 rocks,
20 poops,
and 5 spiderwebs.
(Multiple Runs allowed)"

This task requires you to destroy 50 rocks, 20 poops and 5 spider webs.

Hint text for clue 5:
"Doing something good feels great, right?
You can be proud of yourself!
The final clue is something special just like you!
But in order to find it,
you have to sacrifice yourself inside a room with 6 faces."

This clue requires you to kill yourself inside of a Dice Room. This will spawn the last clue and will revive you of course.

Final Text:
"Good job!
I'm very proud of you!
This is the end of this journey...
but another one awaits you as a custom challenge!"