So I'm seeing a lot of bad and superstitious advice being given. I've brought 2 clerics and 3 druids here now. I can promise you non of these tricks below work. It's pure coincidence when it "appears" to work. It is 100% RNG and your luck. I spent quite a bit of time there on 1 cleric and 2 druids. The other cleric and druid were in and out. I've seen the spawn cycles soooooo many times.
For ease, I like to sit on top of the tower edge where I can see where the goblins (PH's for tainted) spawn. I use pacify/harmony line of spells so I can pull singles. Once I clear them, I either med up or kill some of the deepwater goblins below of the same name as the ones on top (if I have the Mana and I'm bored. Mind you not the aqua goblins.
If the tainted goblin spawns, it does not matter where or how you kill it. The corrupted shaman is not guaranteed to spawn at the tainted goblins death. However when it does spawn, it's guaranteed to drop the quest piece.
Recommendations: EB item (worn effect) Druids/Clerics can wear Lodizal Shield. You could be down there for hours.
Ask a friend or guildee to give you a kei there.
Use root or snare as goblins will run when low health. They can heal but I believe the tainted and corrupted don't heal. I pretty much go nuke mode with a friend or 2.
P.S. if you are having trouble finding the underwater tower there are 2 tunnels under the lake that lead to it. From the west and east of the tower on the other side of the islands to either side. If you zone in from Rathe mountains, just head west under the water and you will see it. If you zone in from south katana, head south until you are adjacent to the tower on map, then east until you see the tunnel.
Hope this helps dispell the illusions being presented. Happy hunting for anyone in the future looking up this mob.