I added a new special level generation table to the
Levels page, including the depths in which they spawn.
The information there is based purely on my observation and the ranges (especially of the later special levels) may be incorrect sometimes - I wrote it down to the best of knowledge. Feel free to correct any errors I may have made.
EDIT: I guess I have too much time on my hands, as I rewrote the
Badges as well. This time, I took the requirements straight from the game, so the badges should be as accurate as possible. But still, please proof-read and correct any errors I made, or any badges I happened to miss.