Get an enchanted amulet, ring, or other item you can enchant with Water Breathing. Make sure it is a constant effect. Put on the item with Water Breathing and jump in some water. Swim to the bottom and continue 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. Another way is to 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. Then, allow the game to idle like this.
Go to Lake Rumare around the Imperial City waterfront and swim under the water for a bit to find a huge rock. Go as far down as you can against the rock, then tape the Left Analog-stick Forward and allow the game to idle. Your Athletic skills may increase significantly. Make sure you are at a location on the rock where you will keep moving straight into it.