Turtle hunting-my all time favorite.
I've shot a LOT of turtles with a Glenfield Mod 25 and Ted Williams 7/8" 4X scope.
I've also shot a lot with a 22-250 off of logs at long range.
If I was going to get a turtle gun I'd put a 10x or 12X scope on it. I wouldn't go more than 14X because you'll likely end up leaving it set on a lower power so you can get on target at close range faster. Less than $250 for decent glass for a 22. Even the Tasco Varmint/target scopes are good enough for under 100yds turtle shooting like you are doing. If you can get a scope with 1/8MOA adjustments even better.
Platform would be a Savage Mark II with that wood thumbhole stock, 77/22 or T-bolt heavy barrel. The Remington varmint/target or a 10/22 with a heavy floated barrel would be good choices for a semiauto platform.
Bipod of course, mine would be tall so I could shoot from sitting.
Ammo is probably the most important component. If you can afford match ammo all the better. But you may be more inclined to use cheap ammo. If so, It is worth the time to experiment with modifying the noses to see if it tightens things up.
Paco Kelly makes a tool and so does Waltz. Here is a thread on castboolits about a homemade job that seems to work rather well and there is discussion of the other tools also.
My 22 wide flat nose tool
There are other threads in the rimfire section that discuss these tools, this is only the most recent.
I will tell you from experience that just nipping, filing, or flattening the nose of cheap ammo will often make it shoot to near match standards.
Have fun shooting them fish eating devils.