This is a fairly straight forward trophy. Early on in the game you can unlock the "Elephant Rider" skill and once unlocked you can mount any elephant you approach by pressing
once you have your elephant simply attack enemy troops using the
button and you should get the ""Elephant kill" bonus.
I would suggest just using any elephant you find and this trophy should unlock naturally with very little effort. You fill find they become a bit of a bullet sponge and don't fair well against frequent car rams so you might find your elephants dying on you as you go.
Here is a video of me unlocking it with my final few kills.