$data_animations is what stores all of the battle animations, it isn't dependent on any additional script. This is more likely a case of the anime_id being out of range. If you have 200 battle animations in your database then anime_id should be between 1-200 but if anime_id is greater than 200 then it'll try to find a battle animation that doesn't exist (like $data_animation[201]) which is nil which causes the error.
Does this happen with every skill? What about when you do a normal attack? Ace will change the animation used by a skill if it is deleted to none so this is probably a misconfigured script that allows setting an animation to play when a skill is used without setting it in the database.