Enter your name as SPELUNKER to play Spelunker Mode. In Spelunker Mode you'll die if you get hit once. There are a few dialogue changes as well.

Another way to activate Spelunker Mode is to start a game in From mode. A Spelunker is trapped behind a bush in the northwest corner of the map. Free him with the Flame Wand and talk to him and you'll be able to choose Spelunker Mode from the main menu.