The game’s whimsical soundtrack (by Harumi Fujita) is crucial. Crackling usually means your emulator’s SPU (Sound Processing Unit) settings are too aggressive.
Tomba! uses all eight directions of the D-pad (for grabbing trees and swinging). Do not use an analog stick for movement unless you set the deadzone to 0%. Connect a USB controller (like a DualShock 4) and map the D-pad.