They will want a camera with good tolerance to humidity + precipitation (so a camera with a proper O-ring seal, and pack it with regularly-dried silica gel). Elephants will likely have a go at the cameras - so they will want to think about protecting their cameras with heavy-duty steel security boxes (perhaps with welded on spikes, which has worked in Thailand) and minimising smell left on and around their cameras during setup (e.g. use gloves, don't smoke or leave food).
Apart from that, the usual considerations apply: good detection circuitry (less of a problem if targeting elephants though, as they are massive) and battery life always helps.
Laila Bahaa-el-din et al. used Panthera and Scoutguard in Gabon; the Goualougo Triangle Ape Project in Rep Congo uses Reconyx I think; Julia Gessner et al. used Reconyx in Rep. Congo and Cameroon. The latter reported that (of 47 cameras), 4 were taken out by elephants and one by a leopard!