Get an enchanted amulet, ring, or other item you can enchant with Water Breathing. Make sure it is a constant effect. Equip the item with Water Breathing then jump in some water. Swim to the bottom and just keep swimming into the floor. Your Athletics will greatly increase in five minutes.
To master your Athletics skill, go into the corner of a room and shut the door if one is present. Alternately, get a water breathing ring and stay under water. Once in the room or under water, tape the Left Analog-stick Forward, to force your character to keep running forward. Allow the game to idle like this.
Go to Lake Rumare around the Imperial City waterfront. Swim under the water for a bit to find a huge rock. Go as far down as you can against the rock. Tape the Left Analog-stick Forward and allow the game to idle. Your Athletic skills can increased by a lot. Make sure you are at a location on the rock where you will keep moving straight into it.