Long weapons are bad
A lot of answers agree on spears or longer swords in this setting, but in reality, they are perhaps the worst choice you could go with. The longer your weapon, the greater mechanical disadvantage it suffers when trying to maneuver it. A long weapon is like a giant lever. Your hands move just a little bit to make the head of the weapon travel a much longer distance. This means that the effects of drag acting on the distal end of a long weapon are multiplied by your mechanical disadvantage. In the air, this mechanical disadvantage is negligible meaning you can turn your weapon faster this way, in the water, this effect is enough to make long weapons turn noticably slower. Especially more proximal heavy weapons like spears and swords which lack the distal inertia to power through the resistance. This all means means longer swords and spears will be especially easy to block or just plain out maneuver.
Also, because you are floating, how strong you are does not entirely matter unless you get into a grapple. As you maneuver a long weapon, every action has an opposite and equal reaction meaning that it's not just your spear turning, but so are you. The power from any melee attack can be summed up as coming from three basic sources:
- The speed to which you can accelerate your weapon.
- Your weapon's inertia. Note, it is inertia and not mass which matters since a distal heavy weapon generally has more inertia for its mass because of its mass distribution.
- Your ability push your attack through your opponent once contact is made.
In water, you can not accelerate to the same speeds as you can on land. While some answers cite spear fishing to justify a spear, this activity is done from out of the water, and used to hit fish that are only a few cm below the surface. If a fisher man were to try to throw a spear under water the resistance against his arms would make getting enough speed to pierce even a fish more or less impossible. This is why divers in the water often use harpoon guns or boom sticks in lue of actual spears to protect against sharks. If a traditional spear were an effective weapon under water, they would not choose these single use spears over a reusable one.
Aa for inertia, a distal heavy weapon will better punch through the drag of the water, but distal heavy weapons also takes significantly more energy to get moving in the first place; so, they generally become impractical at lengths greater than about 1/2 that of a comparable proximal heavy weapon. In this setting, you can not so much make a distal heavy weapon longer than a proximal heavy one, but you don't need to shorten it by nearly as much to make it useable.
Lastly, in water you can not plant your feet to drive your attacks through your opponent using your body weight. With no ground to plant into, once you make contact, most of your additional force will be lost pushing the two fighters apart instead of punching through.
Because of how these 3 factors work together in water, even the lightest of armor would become adequate to stop any spear or sword attack and most wounds made to exposed flesh would be superficial at best. However, these effects on common land weapons are the exact disadvantages your hydromancer is looking to exploit. So what he needs is weapon that overcomes or minimizes these disadvantages.
Shorter weapons are better
The biggest disadvantage of a shorter weapons on land is that you have to get past an enemy's longer weapon, but since the water makes this relatively easy, the advantages that shorter weapons have start to come into play.
In the water, you don't have anything to brace yourself against to generate a powerful thrust or cut, so you need to grapple an opponent to immobilize 2 opponents relative to one another enough to deliver a particularly deadly strike. Since this puts you in very close quarters, a short thrusting dagger is good because you don't have to worry about your enemy becoming so close that you can't aim your weapon's tip into them.
Another tactic to consider is the use of a short sword that specializes in draw cuts like a scimitar. While a hewing cut is meant to be done at a distance and relies on the speed and inertia of the sword to cut through, a draw cut can be done in very close proximity and at slower speeds since it relies on the action of slicing across a target to "saw" through them. So even a slightly longer blade that would be hard to point into an opponent can still be effective in a grapple if used this way.
Lastly, a distal heavy blade produces more momentum than it produces water resistance; so, when you do swing, something like a hand-axe will better overcome the water resistance.
The best weapon is the kopis
The kopis was an ancient Greek/Etruscan short sword. Like a dagger, it's blade is short enough to thrust with during a grapple (not to be confused with the longer machaira). Like a scimitar, it also has a curved blade making it great for draw-cuts, and like a hand-axe, it is distal heavy meaning it can be swung relatively well in water. On land, this an exceptionally versatile sword, and unlike many other weapons, it remains versatile even when you are in the water.
As for materials, since you are not spending a lot of time in the water, steel is probably still the best since it takes prolonged exposure to water for it to really rust. If you are looking for a specific historically accurate alloy that a kopis may have been made out of, I would suggest Spartan steel. The Spartans discovered manganese steel alloys ~2000 years before it was rediscovered during the industrial revolution. When added to steel in the right proportions, manganese makes steel harder without making it more brittle. Since Spartan steel also had carbon contents up to 0.25%, a high quality Spartan blade would have been considered on the low end of medium carbon steel... not quite as good as most medieval steels in this respect, but still good enough to hold its edge and form very well when you factor in the manganese. The Greek historian Plutarch also wrote about how the Spartans would intentionally quench thier coins in vinegar to rob the iron of the temper suggesting that the Spartans as a culture knew a lot about tempering which is another big factor in steel quality. Tempering makes steel able to be bent and spring back into its original shape. Between these factors, Spartan steel is actually more similar to modern steel than almost anything you will find in the ancient, medieval, or even renaissance periods.