I was going to write the lyrics too, but I stupidly checked to see if anyone had already done such a thing. It turns out someone did, and it's not very good (in that it completely falls apart after the first four lines), but I'm unable to come up with a better opening line than he did.
Also, I didn't want to listen to the song 700 times to get the rhythm right.
Feel free to filk up the comments if you want.
Edit: Aw, why the hell not? Even if this is horrible, my opening line's different, at least.
Swimming in a dark trench
Talking to tube worms on a steam vent
Starro didn't decompose
Grew another body; made more foes
Hey Aquaman
Junior is his dead son
Watched as Manta ended all his fun
Hey Aquaman
Namor likes to run amok
Orin doesn't flip out like that schmuck
Oh Aquaman
Fish mind-controlled
Mera's his one and only
Fighting crime
The only way he knows
Hook for a hand
Or sometimes it's made of water
He brings down fishy slaught
-er, no retreat
He's not alone
Tempest, his eyes they glowed
And they made things explode
So easily
Aquaman my friend
Don't you let them say you're cheesy
You talk to scrod, but gee, you rule the sea.
Do you still remember
How you made Züm's brain seize
Basal ganglia
In his Martian brain were
Just like parts piscine
And you never caused Max Lord's death
Or fought demented clowns
Swimming powers zoom like
Flash's running thing
[Followed by lots of repetition. Maybe some flute.]