Bones and lungs
In order to support such a large and heavy animal, you'll need enormous and strong bones. Calcium bones would not be strong enough so you'll need something else, probably carbon fiber.
The inner structure of the bones will probably be hollow to reduce weight and latticed to increase strength. You can use this hollow space to house all or part of the respiratory system.
Additionally, this allows you to have a breathing system similar to that of birds, where air is constantly flowing in a single direction, this solves a potential issue that in-out breathing might cause, stagnation.
This kills a few birds with a single stone:
You solve the issue of getting oxygen to the entire body since now you can have the tortoise breathe from multiple parts.
You solve the problem of managing internal heat by having the bones act as a cooling mechanism powered by the air that is breathed.
You use most of the otherwise empty space that the bones will generate
You solve the whole "breathing" issue
The air-filled bones help the animal stay afloat in water.
You'll probably need more than one heart to pump the blood of such a large creature. The blood itself probably accounts for a large fraction of the weight of the animal, so it's gonna be a difficult task.
One idea I can think of is, instead of having a distinct heart or hearts, make the blood vessels able to pump blood themselves. Having regular one-way valves in the tubes, and constricting muscles around them will probably work, the blood vessels will pulsate in a sequence that will move the blood around.
This distributes the workload to the entire system and solves the slight tendency of water to create vacuums above the 10m mark.
This is probably the most difficult part, moving such a large creature. Muscles will probably make up most of the weight of the tortoise just because of the sheer amount of strength needed to move it. Being partly submerged will help ease the load of actually having to hold up the animal, but it makes moving much more difficult since water is so dense and viscous compared to air.
Have it eat algae. Even better is if you have it grow its own food. Algae need water and sunlight to grow, the tortoise has both of those covered: it lives in the water and has a huge solar collector on its back.
The shell would act as a solar power plant AND rainwater collector to culture the algae, it can then slowly eat this food, just slow enough to allow it to regenerate. Whatever biomass the algae on its back cannot provide, can then be eaten the good ol' way.
I already mentioned the shell a lot. The way I see it, it would have to be made up of hollow interconnected cells. The outer layers would need to be at least partly transparent or translucent to allow the culturing of algae in these cells. The shell would also need to have a series of pores, some connected to the cells where algae are grown and others connected to the bones of the tortoise that would be used to draw in air.
On the inside, the shell would need to be supported by rib-like bones for both structural integrity and to be able to draw in the air needed to breathe. The inside surface of the shell would probably be very porous to allow the body to consume the food and resources stored inside.
From your other question, I believe you want to put people on top of the tortoise. The people could exploit these systems to keep clean rainwater. Algae are nutritious, so they also have a food source (just don't overexploit it)
There are too many organs in an animal to feasibly list in this answer. Though I believe most of them can be distributed into a number of smaller organs, even the brain can be distributed through the body.
A few other details
Given the structure proposed and the way things would work, it will probably be best if the tortoise is mostly flat, that is, only a couple dozen meters high at most. This way you'll have a lot of shell area, which is very important here, very close to most of the body. It also eases on the load of having a lot of organs on top of each other, crushing each other.
It also makes the floating more stable and the structural load lower.