First Golden Banana[]
Run into the Japes lobby loading zone while touching the GB. This cutscene skip is very tricky becasue it requires a certain angle to roll toward the loading zone.
Diddy[]
Don't activate any warp pads before going through the tunnel in Japes. At the end of the tunnel, there's warp pad 1 just a few steps behind the trigger zone for a long cutscene with Diddy shouting for help. You can skip it by kicking or rolling onto the pad, which will cancel the cutscene with Squawk's explanation on bananaports.
Lanky[]
Make sure you have just one melon slice left in Lanky's room. Stand near the red water and pull out your gun. Press C-up and aim horizontally at the switch. Press C-up again, shoot the switch and immediately walk into the water. Lanky will be freed while the death cutscene is playing and you'll get warped to the entrance the level. This skips part of the Lanky cutscene.
Chunky[]
If you enter Factory with Lanky and Squawks has not talked to him yet, you can skip the cutscene where Chunky asks to be freed. Run down-left and do a long jump just before the cutscene plays. You will land in the Squawks trigger zone and he will start talking to you, interrupting the Chunky cutscene.