Just cause a earthquake
While a vampire is exposed to the sun, put a meteor in front on the sun to complete
Pocket veto
There is no specific way to beat any of the episodes per say as they are all features of the overall application. Episode 8 allows you to hold a pygmy above the water and the shark will jump out of the water and eat him. The latest updates can be found here as well http://appmodo.com/522/pocket-god-episode-17-return-of-the-pygmy-now-available-fight-with-spears/
shake the rattle
Killuah doesn't pass the exam; he actually fails it. It happens around episode 30.
The crossroads of destiny
Episode 115, Shippuden right after the intro
Most animals do not pass through four stages of growth. Butterflies, moths and mosquitoes are the common organisms that pass through the four stages of growth.
The Delaware River.
I think you might be talking about Pass - Veto - and Pocket Veto.
The serpant's pass.
you ckike on the girl.