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1.
Someone who is not only beautiful, but wild and troublesome as well. A person labelled crazy beautiful surely has many personal issues or problems that are known to the public and might be deemed crazy, while they are prominently beautiful people on the outside.

"She's a wild one. Yea, crazy beautiful."

Paris Hilton, Lindsey Lohan,
by Yvette83 January 02, 2008
 
2.
being amazingly beautiful; having large amounts of beauty.
Kirsten Dunst was crazy beautiful in the movie Crazy/Beautiful.
by Becky Simms March 21, 2007