Tortles make great grapple monks, thanks to not needing dexterity for armor class, same with making good druids because they don't have to worry about the armor restriction. Anything that uses strength is also good, I have a tortle ancients paladin I'm pretty happy with in AL.
The fluff about them works fine for a paladin, which is backed up by the Alignment section. +2 STR +1 WIS is a pretty good fit though not perfect. Claws and hold breath are more of ribbon abilities - nice in the rare cases they come up. Natural armor is a benefit for first and second level paladins as it gets you to AC 17 sooner, but a detriment to higher level paladin, say 5th or higher, because it's lower than plate and you can't find magic armor. Shell Defense ... might be useful if you're about to drop and instead of attacking you want to try to preserve your auras.
They make perfectly serviceable paladins, but not perfect ones. Which is fine.
STR-based rangers. Or if you use an alternative version with a beast companion that doesn't use your actions then Shell defense lets you turtle up (okay, I admit it, pun intended) when hurt while your companion still goes to town.
Barbarian - great AC, STR, what's not to like. Sure, CON would be better than WIS, but WIS never sucks.
Clerics that don't get heavy armor but do extra weapon damage at 8th. Few +2 WIS races, +1 with some extra goodies isn't a bad fit.
Actually, Druids might be better than clerics - with the metal restriction they normally have to deal with Tortles will get a better AC then most druids, even better then if they had the barkskin spell up. +1 WIS still good. +2 STR is not useful for them with Shillelagh, but can be flavorful in terms of a druid with athletics being unusual. Moon druids could like having a high AC when not in wildshape, other druids could like it all the time.
Monks, for a better AC until your unarmored AC bypasses it. But mostly so you can name yourself after a Renaissance painter and wear a brightly colored mask. Okay, I'll show myself out. Actually, if you don't need DEX for AC, all Martial Arts does work fine off STR. So it's actually a reasonable if unusual build. Go Kensei (XGtE) and a d10 Versatile weapon and it's like you maxed your Martial Arts die.
Hmm, the AC might be of interest to wizards and sorcerers even if the ability scores don't line up. Being armed for OAs while not having to carry a weapon so you have a free hand for casting is nice too. I think I'm just stretching now.