The best way to define it is to break it down. The definition of Legend is a non-historical or unverifiable story handed down by tradition from earlier times and popularly accepted as historical (freedictionary.com). The word “ Tripping” by definition refers to the reaction a person has using drugs, but in this case Tripping is simply the word "trip" expanded, which is a journey which takes you to another place (urbandictionary.com).
My definition is simple. Legend tripping is to go or participate on a quest or adventure for something which has defined a mystery or legend and not verified or explained by science. These legends are cryptids (Bigfoot, Skunk Ape or the Loch Ness Monster), the paranormal (Ghosts and Haunted Houses), extraterrestrials to include UFO’s and lost treasures and places of wonder.