Punching, dashing, climbing, jumping, sliding and running will all level the athletics skill. As long as its hitting your stamina, it should be working towards more athletics experience.
With punching, you don't have to hit anything. Sliding is achieved by crouching while running. Dashing is achieved by double tapping a direction (or double tapping crouch while moving in a direction).
Having the double jump leg mods and using liberal use of the double jump and parkour actions available in the game will also help you get around while levelling up your athletics.
Dashing in particular will give regular experience for the number of times you need to dash each time - in my last playthrough I found myself dashing constantly around whoever I was supposed to be following during all of the "walking" sequences rather than trying to walk and this gave quite a lot of experience quickly.