How do you level Athletics in Cyberpunk 2077?

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.

Based on personal experience, it's a difficult skill to level. You have to run for a certain amount of time (~30 seconds) without breaks, and jumping or sliding (by crouching while running) help. Effectively, you have to treat it like a parkour game and find new ways to quickly move around. Jumping onto and off benches or low walls seems to help too, as it becomes easier to run uninterrupted if you can get just above most of the crowds.

I've also found that the risky behavior of bringing a fist to a gun fight helps cross-train the skill with street brawler, because I'll be running and sliding between cover and my next opponent, but it's much slower than focusing on running itself. The short answer is stop using a car or fast travel and just run everywhere.