Elephants are not supposed to be sent into battle one by one. You need a decent number of them to do real damage. Making them resistant to monks will make them way too OP, especially if your civ’s pike/halb line has weak upgrades. Also see below from other topic:
Elephants need support units. The whole point of this game is creating a well balanced army, not single units. If you want to play single units, play team games only and get your team mates to cover your weaknesses. Otherwise you need to make support units. E.g. Elephants, scorpions, skirms or any kind of Gold unit/siege/trash composition which suits your civ.
Elephants are supposed to be a game finishing unit. The best way to use them is to start with ranged units as an opening, making him counter with skirms or mangonels. Hide your stables either in your base or somewhere sneaky on the map like the corners where your opponent won’t look. Build up your elephant numbers from multiple stables and get all your upgrades. Pre-attack him first somewhere with your ranged units left over and force him to react to your crossbow. He will then move his army over to that side of his base to defend. Meanwhile you send your 30 or 40 fully upgraded elephants to the opposite side of his base. If he’s not paying attention, he won’t realise the 2nd attack notification is somewhere else in his base and by the time he realises it will be GG. If he hasn’t scouted your stables, he won’t have tech switched into pikes/halbs so even when he sees your elephants arriving he won’t have time to transition into them. Obviously if you do scouts / knights opening it will be easier for him to counter your elephants because he will already have pikes + monks on the field.