Rent a dumpster to haul away the concrete after your remove it from around the above-ground pool.
Roll a wheelbarrow to the concrete slab. Use it to throw broken pieces of concrete into as you chip the slab up.
Put on steel-toed boots, safety glasses and a dust mask for protection.
Hold a jackhammer upright about 2 to 3 feet away from the above-ground pool and break up the concrete slab in a circular motion around the above-ground pool. Throw freed pieces of concrete into the wheelbarrow as you work.
Continue to chisel the concrete with the jackhammer away from the above-ground pool in larger concentric circles once you've completely encircled it about 2 to 3 feet away from the pool's walls.
Use a chipping hammer to break up the remaining concrete near the above-ground pool's walls. Do not use the jackhammer near the walls because you might damage the pool. Chip away at the concrete to make it come loose, then pry the broken concrete away from the pool walls with a pry bar and put them in the wheelbarrow.
Break up any large pieces remaining on the ground with a 20-lb. sledgehammer. Throw the pieces into the wheelbarrow and empty into the dumpster as needed.