Skipping the helicopter saves about 5.5s but is not recommended for beginners. See the video below for a tutorial. If you don't go for it you can spit a monkey into the water and bounce off of it to get to the helicopter without fluttering.
The easiest way to navigate the end of the submarine section is to damage boost through the last spikeball, but with some careful camera manipulation, you can barely get past the spike without getting hit. 
Shooting the frog and bouncing off it in the last room saves a bit of time since you spend less time jumping up the stairs.
The submarine can be skipped by doing the tongue glitch in this level. To perform the trick, you first need either a pow block, or a big egg. Big eggs are recommended as there is no known way to consistently get a POW block. See below for setups on keeping big eggs from 2-7 into 3-3.
In the 2nd screen of 3-3 with a big egg, grab an enemy, throw the big egg into the air, and spit out the enemy right before the big egg lands. This will activate the tongue glitch.