This achievement can be annoying.
First of all you won't get the achievement for summonig Elephant as a druid. To get this achievement you need to play as druid or hire druid hero and they level him up and buy "befriend animal" skill. Then you need to use it on a elephant during a battle. I'm not sure if it need to survive said battle because I've got it with the elephant surviving so better to keep it alive.
The bigest problem is that spawned elephant on a map is random and in my case they were pretty rare. So when you find one better save before going to battle.