This is a really substantial undertaking that will take a lot of planning, but C2 works just fine for it. If you're unaware of what a state machine is, google it and look up how that all works. Your 'turns' will be a series of functions triggered by a state machine with timers and such. Your moves, stats, and all that are likely going to be held in a dictionary object or an array. I, personally, use a large array for all of my game data with a matching google spreadsheet that I use for reference. I use that same array to keep track of every quest status, inventory, game progress, save data, and more in different columns.
Enemies are either sprites or containers with multiple sprites controlled by a series of events. You'll probably have two version of them--one on the overworld, one that is controlled by your state machine in your battle system.
Weakness, stats, and all that are going to be equations you come up with calculated using the values in your dictionaries and arrays.
It's complex and there's a reason you don't see as many of them made--particularly in beginner-friendly engines like C2. They're perfectly doable, though.