A jump is not actually defined by when your character jumps, but by when you press a button that causes the character to jump. This means that we can still get more jumps even while the game is still loading right after you die.

Currently, there are 3 buttons that make the character jump: W, space-bar, and the up arrow key. Each of them contributes to the total jump counter when pressed, so you can spam all three at the same time to maximise your jumps per minute.

There's no strategy to get the death achievements, just get the first white orb, then run to the newly spawned red orb, and repeat as much as neccesary.