1. Start with swimming fins, but for the other appendages. Gloves with long (plastic?) claws, with a stretched membrane between them. Works on the idea of foot fins; elongates the hand and adds more surface area to move oneself with.
To add to the hand idea, one could make the 'glove' part extend
up to the elbows, and add fins to the sides of them purely for style points.
2. Include a tube top-ish piece with zippered front and a fin on the back. Style points only.
3. Mask that fits over the head, but leaves nose, mouth, ears, and eyes exposed. Put earfin-ish things behind the ears, and a fin on the scalp. Also, leave enough room inside the mask to possibly fit the small kind of goggles on the eyes before putting the mask on.
4. Everything that can be added to the costume without causing too much embellishment or harm. Include leg and arm bands, and if it would really work and not freak out the wearer (or observer), a fin affixed to the buttock part of the swimsuit.
Great for pool play, scaring the kids, and enacting imaginative fantasies based on "The Creature From the Black Lagoon." Hand fins might not be so good for grabbing, but they can always be removed.
A no-no for anybody who doesn't like spandex, or drawing attention to themselves.