There are a lot of the winged insects that lay egs inside other insects. Maybe some freakish viral infection long time ago carried over lots of dna of the host into the parasite egg.
It's still insane but at least it's imaginable.
The eggs are then produced by the "adult" form, and the process continues.
It's easier to do with smaller animals. The process is also simpler (grow new "adult" as a parasite of the "larva"). The caterpillar to butterfly change is much more complex.
Basically, every cell in the hydra knows how to become a new hydra. What prevents a single hydra organism from trying to become a thousand hydras is a dual chemical gradient. The head emits one chemical, the tail emits another. Cells respond to this gradient depending on how concentrated it is in one particular direction
At the "head" end, the "head" chemical is very strong. Those cells respond by being the "head". At the other end, the "head" chemical is very weak (and the "tail" very strong). Those cells respond by becoming the appendages.
If you chop a hydra in half, the gradient becomes altered. On one half of the hydra, there is only "head" chemical diffusing. The other half only has "tail" chemical. These changes in chemical gradients signal the cells to start producing the parts of the body that were just lost. Eventually, you end up with two identical, smaller hydra.
Theoretically, you could keep chopping hydra in half and keep getting identical, smaller hydra. Obviously you hit a point where you are just going to kill the poor thing, but in theory it doesn't matter...the hydra will always be capable of regenerating.
Cool, right!