If you're having trouble with this beast, it's likely due to how Shell Shield works. Naturally, as an Aquatic pet, your first reaction is to use flying pets. However, most flying pets use multi-hit attacks. Shell-shield reduces the damage of EACH hit BEFORE the +flying damage buff is account for, resulting in nearly zero damage.
For example, Ti'un's Shell Shield reduces the damage of each hit by 112. If you use a flying attack with a base damage of 150 per hit, you'd expect it to do 150*1.5-112 = 113 per hit, which isn't great, but is ok. However, that's not how it works; it really does (150-112)*1.5=57, which makes your damage almost worthless.
Thus, the trick is you NEED to find flyers that don't use multi-hit attacks. Examples include but are not limited to Gilnean Raven, [npc=62664], etc. The important thing is that their primary attack is Peck, not Slicing Winds (don't use Alpha Strike either, as it counts as 2 separate hits even though it only looks like one). If you look through your Flyers, assuming you've leveled enough, you're bound to have some with abilities like these, even though Slicing Winds is more common.
The positive note is, the turtle usually doesn't hit all that hard. He seems to basically do /cast random, so you can have RNG factors here, but he spends most of his time using Tidal Wave, which does only a small amount of damage to each pet. He'll occasionally use Pump; you can't really predict when, but this is the only thing that's dangerous to your frontline pet. However, as a result of this, it is completely reasonable that a single good Flyer will knock out over 80% of his health before dying, so even if you don't have 3 good Flyers, then one good one followed by 2 crappy pets (potentially not even Flyers, as Slicing Winds is worthless against him, flying or not) will work.
EDIT: Forgot to mention, always lead with your best pet on this one. The first pet you send out will be out the longest; Tidal Wave will tend to ensure that your backline pets come out with something like half health, making their uptime shorter. If using a pet with [petability=518 domain=www], obviously put it last to facilitate a finishing blow. That being said, as long as you use Flying abilities that aren't multi-hit, you should be more than fine.
EDIT2: As of 5.3, Alpha Strike only shows up as a single hit on the screen but SEEMS to still count as 2 separate hits.
Elite
Ti'un the Wanderer
The highest voted Wowhead comments for this page. They are community notes, not TheWoWDB comments.
I used the Fire-Proof Roach as my first pet. Used the ability Apocalypse. The ability killed him when the meteor hit, after 15 rounds. I guess any roach or beetle with the ability would do.
Edit: The roach does not have to be alive or the pet in play when the meteor hits btw. (thanks huspomike)
After trying many different combinations, I was able to solo him with [npc=68846] by using [petability=416], [petability=481] and [petability=221].
Details
This roster comes from the current game client's data files, so it is not a complete list of every NPC in the game - older world NPCs that are no longer in the modern client are absent.
Community notes from Wowhead · 463 comments
Top 3 shown aboveThe comments below were written by Wowhead users. They are community notes, not TheWoWDB comments. See them in context on Wowhead.
The top 3 are shown in Top Comments above. Read all 463 on Wowhead.
Level and Map Tracking
The game data tunes Ti'un the Wanderer for level 1.