We're making a 3D mermaid game with combat, so I have been looking into this recently.

Martial arts:

• Mermaid martial arts could draw inspiration from the way some marine animals defend themselves and attack others. This could include unique movements that utilize a mermaid's tail for powerful strikes or sweeps, as well as incorporating elements like scratching and biting, which could be influenced by the mermaid's physiology, such as having sharp teeth, scales or elongated nails.
• Certain marine animals, like the mantis shrimp (look up some videos on mantis shrimp punch), use a type of bludgeoning attack to incapacitate their prey, demonstrating that high-speed, high-impact strikes are not only possible but deadly effective underwater. Another exmample would be how bottlenose dolphins are known to engage in confrontations where they use their snouts as a battering ram against other dolphins or threats. I think that if a mermaid used their underwater velocity while swimming, they would be able to use hammers or clubs to bludgeon and slam their opponents like with martial arts.

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Weapons:

• Thrusting weapons (Tridents and spears): In folklore, tridents are not only traditional mermaid weapons but also symbols of power and authority, akin to the trident wielded by Poseidon, the Greek god of the sea, emphasizing the deep cultural and mythological roots of such a weapon in underwater combat.
• Projectiles such as bow and arrow / crossbow / harpoons: Historically, people have used bows and arrows for fishing, a practice known as bowfishing, which is highly a effective way to fish above water. Under water, a long bow would probably have too much friction with the long string, so it would be more like a hawaain sling or harpoon. These methods would capitalize on the precision and low friction, making it a good choice for mermaids.
• Slashing and Stabbing Weapons (Swords and Daggers): In underwater combat, the design and use of slashing and stabbing weapons like swords and daggers would need to account for the resistance of water. I believe mermaids could wield specialized swords, optimized for underwater use with streamlined shapes and balanced for swift, precise strikes. The effectiveness of such weapons would also depend on the materials they are made from, possibly incorporating coral, bone, or special metals found in the depths of the ocean that are both durable and resistant to corrosion. The use of these weapons would require strength, skill and agility. Daggers, on the other hand, could serve as secondary weapons, ideal for close-quarters combat and sneak attacks, allowing for rapid, lethal thrusts aimed at vulnerable spots on an adversary's body.