Youtube Playlist

Some solutions i took from jumper5989 and re-recorded them to have everything myself and in the same quality.

The following 3 achievement unlock clicking on "Community" in game (custom levels have been removed so they auto unlock instead):
Sharing is Caring - Publish a level
Community Player - Beat a user created level
The Critic - Rate a user created level

Other achievements (self-explanatory I would say):
Let it Go - Restart a single level 6 times in one sitting
Evil Genius - Use the level editor to save a level with every type of object in it
Midnight Lover - Use the level editor to save a level using only black or rainbow tiles