This is something I've been wondering about DKC3 for a while, and after being inspired by the corresponding topics for DKC and DKC2 I finally decided to find out for myself.
1: o x o o o - Lake Orangatanga
2: o o o o o - Kremwood Forest
3: o o o o o - Cotton-Top Cove
4: x x x x x - Mekanos
5: x o o x o - K3
6: x x o x o - Razor Ridge
7: o x o x o - KAOS Kore
8: x o o x x - Krematoa
My own criteria for this is reaching the flagpole then returning to the start of the level. My attempts are all done without utilizing any glitches, although it's probable that some levels may be made possible with glitch abuse.
I didn't attempt any levels that I suspected would be impossible by normal means. (Ripsaw Rage, Krack-Shot Kroc, Buzzer Barrage, Kong Fused Cliffs, Pot Hole Panic, Stampede Sprint, Rocket Rush)
Krevice Kreepers fails because it becomes impossible to return after dropping off the final rope, but it's possible to return to the beginning of the level until that point. Most other levels that fail do so because of a big drop or gap, or cameras preventing backtracking.
Squeals On Wheels only seems possible if you have the final door opened, making it necessary to go through the level normally. You won't be able to return if you use the warp barrel to bypass it.
Levels that were very fast to go from end to beginning were Barrel Shield Bust-Up, Ropey Rumpus, Criss Kross Cliffs and the waterfall levels.
edit: Murky Mill and Tearaway Toboggan added. Thanks Tompa!