In selecting the following levels as "most difficult", I've tried to balance all things into consideration - the stage itself and the extras. Here is my short list for "most challenging level" in Donkey Kong Country 2: Diddy's Kong Quest:
Web Woods (5-5)
Patience is the key in web woods. Lots of enemies and pitfalls, but as Squitter the spider, you can fend 'em off with webs and climb yourself anywhere... But a few things make the level a bit tricker than most.
Chain Link Chamber (6-5)
Screech's Sprint (7-1)
These two "gems" from the DKC2: Lost World get honorable mentions:
*Animal Antics (8-5): Particularly the part where the wind tosses Squawks all over around the thorn maze.