I am running Dungeon of the Mad Mage and my players are on the 8th level (Slitherswamp). According to the campaign book, "Many tunnels and caves of Slitherswamp are partially flooded with water, ranging from a few inches to several feet in depth, over a layer of thick mud". One of my players decided to go all Navy Seal during combat and submerged himself in the water. His argument was that because it was murky water it would give him full coverage. I, instead, ran it like underwater combat (the npc's rolled at disadvantage). He was trying to say that because of the murky water he had total cover (A target with total cover can't be targeted directly by an attack or a spell, although some spells can reach such a target by including it in an area of effect. A target has total cover if it is completely concealed by an obstacle).  The other reason for running it as underwater combat was that they were fighting Bullywug, who have a swimming speed. How would you have run it? 

ALSO: a separate issue had to do with fire resistance. When you are fully immersed in water you have resistance to fire damage. One of my players has resistance to fire already AND he was submerged in water. I do not believe that resistance stacks, but to compromise, instead of half damage I had them take 1/4 damage until I could research more. Is this the right way or is it just half damage (because resistance doesn't stack)? 

EDIT: I found this in CH. 9 of the PHB: Multiple instances of resistance or vulnerability that affect the same damage type count as only one instance. 

My quip at the table would have been, "a Navy SEAL would have washed out of BUDS for not knowing the difference between cover and concealment, I mean even Coasties know that" (I kid, Coast Guard personnel have some pretty cool missions and are by and large a squared away bunch if that broadside rubbed anyone the wrong way). 

RAW Cover is clearly physical barriers, all the examples are things that would stop an attack.  Murky water clearly, so to speak, should be governed by vision and light.  I can't see any logic going the other way based on how cover is described functioning RAW.  Pending on the water and available lighting, I'd rule either lightly obscured or heavily obscured (the latter if the target is full on stealth holding breath, the former if they're active in the water, but that's my judgement call) imposing possibly blinded condition on attacker in the latter case otherwise disadvantage as you ruled.

How is this tactic affecting Rambo own actions?  If he's bobbing to get off attacks without any modifiers, a smart opponent would just ready an action triggered by targets emergence from the water.  Are they just laying low relying on disadvantaged acoustic perception?  

It sounds like he's choosing to be prone (which already does anything that concealment would have given him), though he should probably also get resistance to fire.

You know, you either added or I missed the bullywug opposition.  I'd actually consider granting the DM a wide latitude in this environment since it sounds like the PC is fighting bullywugs in an environment that the bullywug is likely better adapted to.  I'd have filled the environment with frog and toad kin who'd be _noisy_ about the PC granting the bullywug actually advantage against the PC's efforts at concealment.  I'm not 100% there, but I'd to with it.

You're right resistances don't stack.  Also RAW immersion does provide fire damage resistance.  Depending on the nature of the fire (like magical effects), Sage Advice has washed their hands of any house ruling declaring fireball also transforms water in its area of effect to superheated steam that would compound rather than resist damage.  Some folks do house rule that, but it's not RAW, but it is nasty.  

The bullywugs should not have any trouble fighting in water. Was the water actually murky?

If the water is murky it would be obscurement, not cover.