Submarines and aircraft carriers

WWII brought many ways of warfare into the spotlight, changing how we fight.

Submarines were plenty. Sonar might not be the best way to target other submersibles with much of the technology at that time but as the enemy has a floating/submersible city, targeting shouldn't be too difficult. Fire enough explosives under water, which are generally more powerful but with less reach and you can take those things down.

Next is airplanes. With patrols you can have reconnaissance over huge areas. Bombers and fighters have good firepower, allowing them to absolutely wreck the enemy with little danger to themselves. With aircraft carriers and a complenent of boats capable of coastal bombardement they don't stand a chance.

These two should already be enough to make the merfolk that are willing to attack humans extinct in short order, or force talks. They can have valuable resources or work power, which can be exploited in exchange for their lives/homes. Technology is scary and we fully exploited it during the second war. Repeating rifles, chemicals, devastating explosives at short and long range, timed fuses. Basically computerised warfare, rocketry and biological warfare are the only ones that still needed to be expanded.