A contraction of the words legitimate and ridiculous. It's used to describe situations that are both highly impressive and entirely realistic.
Mike: Dude, look at my blueprints for this dry ice cooled gravity bong. It chills the smoke to a lovely 34 degrees so that it finishes clean. You can even add flavors via this secondary bowl for spices and essential oils.
John: Oh my god dude, these are legitculous.
Mike: Yeah, we're going to completely decimate our ties to reality.