For the three Danger Arenas, it should be noted that completing it requires getting to the end of the level without being killed by the red line coming towards you from the left of the screen or by baddies in the level. It is not necessary to kill any particular number, but just to complete the level. My strategy was to run through the level as quickly as I could until I got to the very end and then worry about killing baddies (though you pretty much have to kill them as you are going as well).
Danger Arenas are unlocked next to the Lenny the Lyrebird (he looks vaguely like a blue peacock). In level, they will always be marked as Lenny's Restful Resort. You MUST play them in level or they will remain locked for you on the main screen. If you play them but fail to complete them, you will be able to play them en masse from the main menu. I have written below where to find each of them if you missed them on your first playthrough.
1. Treetop Terror - "127 Minutes" subarea "Lenny's List" -- go straight and then take the very first opportunity to drop down and go slightly to the left and you will see Lenny and the first mission
2. Sleep with the Fishes - "Raise the TYtanic" subarea "Raise the TYtanic" -- first exit from the water, jump through the blue orbs to the lawn chair to more blue orbs to find the mission
3. Dusty Dust-up - "Fair Dinkum Drinking" subarea "Sheepskin Sweatshop" -- after descending through the long mostly vertical rock passage (directly after the first two water troughs for the sheep), you will be able to drop down through a wooden boardwalk and will see the challenge