A tricky race for this class. Looking for suggestions.

I would stay away from cavalier but besides that most things work. I personally am thinking wahammer shield, feats like shield master maybe dual wielder  but lots of good options I think samurai feels right for tortle. good luck 

For obstacles, the big one is that the tortle can't wear armor.

So it can't benefit from defensive fighting style. Also can't get better armor as it levels up.

Oh, and no Heavy Armor Master feat.

It's natural armor is higher than non-magic armor (besides plate) anyway.

Heavy armor master and defensive fighting style are only minor losses.

I think they'd make excellent STR based fighters. Samurai subclass can use that +1 WIS. A mount wouldn't handle their weight so well, so probably not cavalier. No DEX bonus, so arcane archer and gunsmith would also be suboptimal.

Of course you could make any class/subclass work if you wanted.

perhaps grappler feat could be used with samurai's rapid strikes feature. giving a pretty reliable additional attack per round.....

also...

teenage mutant ninja turtles....

it had to be mentioned!

cowabunga dude!

They can also hold their breath for an hour at a time.

Could try to specialise in fighting in gas clouds...

You could go with champions and keep him STR based. But Samurai would be awesome flavor 

Shouldn't the defensive fighting style still work since it has natural armor?

Edit: forgot to quote

Quote from Chronocide >>

For obstacles, the big one is that the tortle can't wear armor.

So it can't benefit from defensive fighting style. Also can't get better armor as it levels up.

Oh, and no Heavy Armor Master feat.

 Shouldn't the defensive fighting style still work since it has natural armor?

Quote from cyb3rparad0x >>

Quote from Chronocide >>

For obstacles, the big one is that the tortle can't wear armor.

So it can't benefit from defensive fighting style. Also can't get better armor as it levels up.

Oh, and no Heavy Armor Master feat.

 Shouldn't the defensive fighting style still work since it has natural armor?

 No. Defensive fighting style requires you to wear armor.

Defense

 

While you are wearing armor, you gain a +1 bonus to AC.

My head hurts now.  I have Teenage Mutant Ninja Turtles stuck in my head and it's all y'all's fault.  I'd try and help, but I'd need to know what sort of concept you want to try.  Some would be pretty hilarious if you are looking for humor...  I find the whole Tortle race to be kind of silly, and I don't see anything that could make me take them seriously in a game of my own...  So if you're wanting to be serious, there should be a way, and it would be fun to try and help out.  TMNT started out as an ultra violent comic that got turned into a highly silly children's show.