First, finish Poseidon's challenge before Atlas'. (this is possible with infinite magic, also with regenerating magic if the player is extremely lucky and patient.) As you exit the Chamber of the Eye, the little door you go through won't close behind you. Come back after visiting some other place. You suddenly have an entrance to a half-baked CotE, with only collisions loaded. Jump in the pool and swim out through the floor. Then you're a free man, ready to roam the classy Rings or other fine areas of your choosing... This is the only way I've found to get to swim at the Rings or Atlas' challenge. EDIT: Nope, not any longer.
In all actuality, your choices are very limited. Entering Hades's challenge swimming in the air is not possible, and since you already did CoP (and got the trident), Atlas's seems to be the next logical choice.
The difficulty in moving like this is with the areas sometimes not loading correctly. By moving more carefully or retrying from a saved game or a checkpoint makes things sometimes alleviate themselves.
You can sequence break heavily. You can get the crank, Zeus' shield and get the barred door (at the saw room) open easily. Hades' shield you can't get to, since the area won't load until you drop the stone in there, and you can't pull the switch while swimming.
You can swim all the way through to the other end, but you can't get the skull, nor can you open up the door to the TotE, leaving you stuck in the small strand of corridor where you witness the cutscene. The only place where you can abort your state of "swimmingness" is at the yard where there is a puddle of water. The wet stains at the Atlas-statue's room's floor do not unfortunately count as water.
God of War glitch FAQ: