This was posted by me in resources a while back, but I thought it would be better here. Plus some strats have changed since then.

Basic Strategies

The Stage 4 Glitch: The stage 4 Glitch allows you to complete most of the stages in a matter of milliseconds. To perform it, you simply keep holding down the mouse after you beat stage 4 and drag it for every stage except 28.

Pausing: Pausing is the most integral part of any%. After you beat a stage, the timer keeps rolling, unless you pause the game. For the first 3 stages, beat the stage with one hand on the keys and one on the mouse hovering over pause. Complete the stage, then try to press pause the frame you beat the level (or as close as you can get it). After stage 3, select the pause button with tab and, while performing the stage 4 glitch, rapidly pause and unpause using space/enter once every level so that it will complete each level in a fraction of a second each (in-game time).

More Complicated Strategies

Stage 4 Glitch Optimization: When you perform the stage 4 glitch, don't just use space to press pause. Use space and enter at the same time. (It might take a few taps, but it'll work.) This will let you complete the stages in only .05 seconds each. (This is, so far, the lowest possible time per stage.

Stage 28: The strats for this stage have evolved from when I started running this game. When I started, I thought the most optimal way to beat it was to do it legit, but since then, the helpful DHA has completed a run using the stage 4 glitch. It seems to be completely random whether you get it or not, but something he said to do is hold right while you're dragging. I have successfully pulled this off once. That tells you how frustrating this can be. Good. Luck.

Early Stages: The average time the timer should read after stage 1 is about 1:40 (one, of course, being seconds.) The fastest time I could ever reach completing stage 1 is 1:22, so that's god time. Here is the method I use for the first two levels: As the elephant is being dropped from the pipe, start moving before he hits the ground, but not immediately, then as the elephant bounces forward from the ground, it will let you jump after hitting the ground. This lets you get to the platform extremely quickly. This goes for stage 2 as well, albeit reversed controls. As for stage 3, all you really do is hold up and right as the stage starts, but before he hits the ground let go of up and keep running forward to the pipe. This, combined with precise pause clicks, will achieve a very fast time in the first 3 stages.

I hope these tips will be of use to you in the future if you decide to run any%!