Adding anything that forces the player to think (even for a second) is usually a step in the right direction.
- Maybe a tree/plant type enemy that, if attacked with fire with violently burst into flames (either damaging enemies which is helpful, or damaging your party which is not).
- Maybe a mushroom that has a chance to poison/paralyze/sleep you if you attack it up close (forcing ranged attacks).
- Other games add features where chaining elemental attacks gives bonuses, like dousing an enemy with a water attack, making a subsequent lightning attack more powerful.
- An enemy that starts buffing the enemy party if it's still alive after a couple of turns.
- Maybe a troop of two, with one enemy acting as bodyguard over the other. You can attack them both, but the bodyguard will fly into a dangerous rage if you damage/kill the enemy they're guarding.
Oh, also try to make all of your skills/spells useful in some way. Instead of a weak and strong ice attack, make the weaker one have a chance to freeze the target for a turn, while the powerful one has no side effects. Maybe a weak wind attack also boosts the user's agility, making him attack earlier next turn. If your elemental magic is in tiers and they all just do damage for varying MP costs, most players will abandon the weaker versions after a while. If the weaker ones have some kind of potentially useful side effects, then they are more justified.
Also status effects. Make them work on bosses! Most games have state-inducing skills just inflict a state without doing any damage or anything. Purely utility. Thing is, during regular battles, you're usually better off just attacking, and on the only enemies where it would be useful (bosses), they're all immune! You can get around this even if you're just using regular states and no scripting. Make a poisoning skill inflict two poison states: one that does the normal 5-20% max HP damage per turn, and one that does only 1-2%. Make normal enemies immune to the weak one, and bosses immune to the strong one. Little tricks like that can go a long way.
But yeah, anything that makes the player maybe not want to just hit attack every turn is something to consider. Balancing battles is not everyone's forte for sure. Good luck!