Animals that can withstand literally astronomically high accelerations

It's not about cheetahs. In terms of accelerations, cheetahs are pathetic. There are animals out there designed to cope with astronomically (I do not use that word lightly) high accelerations.

A tiny reptile called the rosette-nosed chameleon holds the current record among the animals that give birth on land, meaning reptiles, birds and mammals. It can flick out its tongue so rapidly that it briefly accelerates at 2,590m/s/s - about 170 times faster than the 15m/s/s maximum acceleration of the cheetah or the peregrine falcon.

25 g ? YAAAAAAWN.

Muscle simply cannot accelerate at these astonishing rates. No matter how finely-tuned or powerful a muscle is, it can never contract quickly enough. However, a contracting muscle can instead stretch an elastic structure and hold it in a stretched state – or, better still, keep it stretched with some sort of latch. When the latch is released, the elastic structure snaps back into its normal length. This releases energy so explosively that a small and lightweight structure, like the chameleon's tongue, can be accelerated at a tremendous rate.

Paradoxically, it might be precisely because reptiles and amphibians are sometimes slow and sluggish that they have become kings of acceleration. If the ambient temperature is cold, their muscles are generally cold, stiff and slow to respond. Elastic structures offer these animals a way to catch a meal even when their muscles are cold. These elastic structures show less of a drop in performance with temperature than muscles do.

...Those first measurements, taken at 5,000 frames per second, showed that peacock mantis shrimps could accelerate their clubs at an eye-popping 104,000m/s/s; comfortably 20 times as fast as any amphibian or reptile.

10,000 g ? I suppose that's more respectable.

Like the mantis shrimp, the trap-jaw ant hauls open its jaws using muscle power, stretching elastic structures in its head in the process. When that elastic energy is released the jaws shut. Perhaps partly because those jaws are operating in air rather than water, and so meet less resistance, they accelerate faster than mantis shrimp clubs. They reach a peak acceleration in the order of 1,000,000m/s2: ten times greater than the shrimp.

OK, 100,000 g, now we're into truly scary acceleration levels.

Paradoxically, super-fast weapons are very slow. Spearing mantis shrimp such as the zebra mantis shrimp have mouthparts shaped like tiny, hydrodynamic javelins... They use these sharp javelins to pierce the flesh of passing fish. Fish can clearly outpace snails, so logic would suggest that spearing mantis shrimp accelerate their streamlined weapons at rates that far outpace anything seen in smashing mantis shrimp. But they do not. In a 2012 study, Patek and her colleagues discovered that spearing mantis shrimps achieve peak acceleration rates about 100 times lower than their smashing shrimp cousins.

A spearing shrimp must react quickly when a fish swims near enough to become a target. It needs a weapon that can be primed and fired quickly. So spearing shrimps have sacrificed one kind of speed for another, ditching speed of weapon acceleration for speed of weapon priming. . "It takes a lot of time to be ultrafast," Patek has written. But when circumstances allow an animal to become super-fast, the rewards can be enormous.

However, it is not clear whether or not this "you have to be slow to be fast" idea plays out in all circumstance. Impressive though they are, the 1,000,000m/s/s accelerations achieved by trap-jaw ants are no longer world-beating. Their record has been blown out of the water by the humble jellyfish.

When the cell is triggered and that elastic energy is released, a microscopic harpoon-like structure shoots out of the [jellyfish's] nematocyst. The harpoon can reach peak accelerations of about 50,000,000m/s/s: 50 times the peak trap-jaw ant acceleration.

OK, 5 million g. If sustained that would be the speed of light in about 6 seconds, ignoring relativistic effects. There's surely a good plot device in there somewhere.
http://www.bbc.com/earth/story/20160916-how-some-animals-accelerate-faster-than-all-others