I'm pretty sure this achievement is practically unmissable, because I believe the Oliphaunts must be defeated to progress in the level, but I suppose it could be missed if you're playing in co-op and your partner eliminates all the opportunities to unlock it.
In both the end of 'The Dead Marshes' and 'The Battle of Pelennor Fields', you'll fight several Oliphaunts which resemble- you guessed it, elephants. In 'The Dead Marches' you won't be playing as Legolas unless you're in free play, so 'The Battle of Pelennor Fields' is where you're most likely to unlock this achievement.
Some Oliphaunts on 'The Battle of Pelennor Fields' have weaknesses to Aragorn's sword and not Legolas' bow and therefore won't work. Other Oliphaunts have pegs on their legs for firing arrows into to swing off of. Do that, and climb up the creature, eliminating all opposition up top. Once you defeat all the foes in the riding the Oliphaunt, the poor creature will flee and the achievement will unlock.
As unlikely as it is, if you do miss this achievement because of a co-op partner stealing all the kills, reenter one of the two previously mentioned levels in free play, select Legolas, and kick some Oliphaunt butt.