I might have a bit too much saltwater in my brain. I'd like to discuss (can you do that in this format?) the ideas of combative mermaids on land. If you saw my other questions, you saw me bring up Tactics Ogre Knight of Lodis as a cool inspiration for this.
Bryan McClure had a good comment in this question thread: Mermaids on Land?
The focus here is land combat, but sea combat may come up as it will effect mermaid military culture.
Movement
Crawl
As was delved into in the linked question, mermaids aren't the most agile. Their crawling speed would be in the neighborhood of 5, 8, maybe 10mph. To compare, the average human runs (sprints?) at about 15mph. However, they need to use their arms to crawl like this, making it combat ineffective. They might be able to hold a weapon while doing this, at least. Crawling with one hand or even crawling backwards is probably possible, and you can use a weapon while doing this, but it would not be easy.
Slither
Mermaids could also move with just their tails, while their human upper-body is upright. However, this is much slower. Still, it will serve as a pretty stable platform for fighting, possibly more so than a human's stance.
Quick Step: They could, in fact, curl up their tail, and make one "quick" "step". A little like a snake coiling before a big movement, but much less so.
Sidewind
Mermaids might also be able to do something a little like this, but again much less so. It does mean their sideways motion will be faster than their backward and forward motion, when moving with just their tail.
Spring
Due to their light weight, and presumably very strong tails, mermaids will likely have a very strong jump, where they can spring at you or into the air. That is, if they can get that energy shaped into a proper jump. This could be useful in a few ways.
Roll
Like people, mermaids could make use of a log roll. They might even be able to tumble forward or backwards, with some practice... possibly. This can be useful for quick, desperate, defensive motion.
Spears
These will likely be the most popular weapon with mermaids. They give them reach, which helps to make up for their lack of mobility, and are pretty useful underwater as well (so they'd have practice with them). They can also be thrown?
Thrown
I don't see why not. The mermaids have the upper body for it. While you can't get a run up, then might even be able to snap their bodies with the throw to give it a bit of extra velocity (so it might be more than a standing throw for a human, but less than a human with a run up?). Of course a mermaid would want more than one spear if they're going to be chucking them, and carrying around a bag of spears is rather cumbersome.
Tail
The tail itself is actually a reasonable weapon, for the mermaid. If they swat you in the back of the leg with this, you will fall down. If they smack you in the head with this, you will surely feel it. They can swing it around quickly, and will be rather erratic if panicked.
I can imagine mermaids creating fight-book style techniques, where after parrying a certain blow, you come around and hit them with your tail
Ranged Weapons
Just about all ranged weapons should be fine, except ones like the crossbow that requires you to use your foot to load it. The issue is, mermaids will not have much underwater practice with ranged weapons. You can use a bow or crossbow underwater, at very short ranges. Some mermaids may have practice hunting near rivers, where they come out of the water with some ranged weapon then clock an animal who was taking a drink. Being submerged underwater will be tough on their bows, however, if they use those.
Unless a mermaid commits a lot of effort into learning ranged weapons, it will be trouble, as they will not be used to the physics of projectiles.
Physiology
Posture
Mermaids would be able to assume some postures not practical for humans. Mermaids are bottom heavy, their tail probably weighs a lot compared to the rest of their body. It will also be rather long/large. This means they have a solid foundation to lean from.
Try leaning as far forward as you can, you'll notice your balance starting to give out. Bend in half like you're bowing to the King, and you can walk around and do stuff (like run into things) with reasonable balance; though taking a swing at someone would likely not go well.
Mermaids can likely take these awkward postures easily. A mermaid might be able to lean so far, their body is close to horizontal by the time
Reach
Aside from the reach with the spear, Mermaids may have an amount of reach with their posture. For example, if they "coil" up and crouch down, it will be hard for a human swordsman to reach them as you have less reach down low. But then, when they need to, the mermaid could extend her entire body into a thrust. A small mermaid is probably about six feet long, others being longer still.
As mentioned above with posture, the mermaid might be able to get close to horizontal, which gives them a much longer reach. A human can reach something like 3 to 5 feet if they really lean into it (dangerously). A six foot mermaid would have a reach of almost 8 feet! They may also be less endangered of overreaching, while doing that. What's more, due to how very low to the ground they'll be, to humans it'll feel more like 10 feet. This will make the mermaid with a spear the equivalent of melee artillery. It is also likely to make for a very strong thrust.
One disadvantage to this reach, is it would take a moment for a mermaid to retract herself from this posture. For one thing, the amount of energy and mass involved, it's going to take a moment to fully stop (dissipate the energy) so you can start retracting. You wouldn't want to be thrusting like this constantly.
As a point of interest, since mermaids are used to fighting vertically underwater, fighting horizontally likely won't seem unusual to them.
Prone and "Standing"
If you trip a human, it takes them a moment to re-orientate themselves and get up. Aside from the difficulties of how to trip a mermaid... they could swap between prone and "standing" positions quite easily. If they need to pick up loose change they dropped, easy. If you push them over, they can spring "back to their feet" like a wobbly man.
Armour
Armouring the lower parts of the mermaid's body is tricky, and normally mermaids would wear pretty limited armour underwater. You could combine armour with floats underwater, and take off the floats on land.
They could wear chainmail skirts over their tails. The upper body can mostly be armoured as a humans can be. Of course, if the upper body is too armoured, certain postures will become difficult.
Mermaids would likely wear some armour just so crawling around is less painful, possibly with a thick textile fitted to their tails to prevent chafing. But combat armour, as much as other people avoid it due to discomfort, mermaids would be far more concerned about that. They would already feel weighed down and uncomfortable on land.
Shields
Mermaids would not normally use shields underwater, as they are a pain to swim and maneuver with in water. They may try to learn their use on land, to make up for their limited mobility. Shields aren't difficult to learn the basics of, even if mermaids aren't skilled in their use it should be helpful.
However, that is an extra thing to carry when travelling, so mermaids would likely not be keen on these by and large, except maybe bucklers.
In case of armour and shield, of course, most mermaids would travel by raft, carriage or horse, so weight concerns are less of a problem.
Important point: Since mermaids can make themselves very low to the ground, they could get complete coverage from a shield (as long as no one fires from the side, as that long tail is a target).
Conclusion
Mermaids are truly unorthodox enemies to face. Their oddities and advantages don't necessarily indicate they have equal ground with human fighters on land, but there is enough evidence to suggest they would not be completely helpless.
Mermaids are very defensive fighters, using their reach to their advantage in a bid to scare off opposition. Ranged weapons are their bane, as mermaids aren't mobile, well armoured enough, nor skilled in ranged combat enough to contend with them. Still, mermaids can go prone, can move erratically, spring and roll as necessary, making them very unorthodox targets.
Mermaids could launch surprise raids out of water, from sea or rivers, then retreat back in before reinforcements arrive.
Question?
So, what are your thoughts on mermaids? Anything in this that seems incorrect, or that you would like to add? I'm sorry that this isn't a straight question, but more of a reality check and a request for second opinions.
We should consider taking this up to a chat room (I don't think I have privileges to make one, presently) to discuss it at length (I'd love to go into different types of thrusts and manoeuvres).