I don't play DKC2's Lost World levels as often as the regular levels, and I must confess that I've never been able to remember which level is accessed via which world map... This post can serve as a guide/reminder of which 'lost level' can be reached from each area, and this thread can be for any discussions related to these Klubba-guarded regions. I've even decided to enable a poll, for those who like to cast votes about such things.
Jungle Jinx (via Crocodile Cauldron)
The game's first jungle level; bounce from one giant tractor tire to another across treacherous spikes.
Black Ice Battle (via Krem Quay)
A perilous and slippery descent though a deep ice cavern full of Zingers, Klampons, Spinys, Klobbers, Krooks, and Neeks.
Klobber Karnage (via Krazy Kremland)
Another jungly challenge, this time full of Klobbers & Kabooms... then come the Zingers, the rotating barrels, and (of course) more spikes!
Fiery Furnace (via Gloomy Gulch)
This lava level starts with hoards of Spinys and Klampons, then it all comes down to dodging Zingers using the steerable barrels.
Animal Antics (via K.Rool's Keep)
A notoriously long, difficult and uniquely varied (jungle/ice cavern/brambles) level which allows the animal buddies to do all the work.
...beware the brambles in the breeze!
Remember: Klubba hasn't set up his kiosk in the first or last worlds... only those in between.