The following was done on Snes9X v.151 for Windows and the version of the ROM used was Donkey Kong Country 3 - Dixie Kong's Double Trouble (U) [f2].smc.
1. At the very first portion where Dixie uses her helicopter spin, land to the very left of the Ellie barrel (it's difficult; I recommend using savestates).
2. Hop over the Ellie barrel and grab Parry.
3. Throw Kiddy Kong off the cliff and make sure he doesn't come back.
4. Hop in the Ellie barrel. Parry should be facing the opposite way, and if so, continue through the level.
If done correctly, Parry will completely disappear when Ellie is scared by the Sneeks and Ellie will run backwards!
Below, you'll find steps three and four, along with the savestate.