What do you call the action of alternatively walking and jogging to complete a Full Marathon?

Solution 1:

I'm no runner, I am allergic to any physical outdoor exercise but online I found the following

• Run-Walk

The walk-run intervals in this plan remain consistent throughout (one minute of running and three minutes of walking) up until the race. The second program (run-walk) is for women who currently run-walk or who run shorter distances. Run-walk workouts are running-focused and intervals vary to help improve performance and speed.
Women's Running

from the website Walk Jog Run

The Newbie Run-Walk Marathon Training Program is a very popular program for first-time marathoners and those who want to enjoy training with minimal risk of injury.

New York Times' article

To train for my first marathon, I’m using the “run-walk” method, popularized by the distance coach Jeff Galloway, a member of the 1972 Olympic team.

The OP's sentence

Shree ran-walked her way to the finish line, completely exhausted and struggling for breath.

Solution 2:

The word Fartlek describes the action of alternating speed:

Fartlek is Swedish for "speed play," and that is exactly what it’s all about. Unlike tempo and interval work, fartlek is unstructured and alternates moderate-to-hard efforts with easy throughout.

^{_{Source: Runner's World}}

The previous quote suggests that this is a method of running, but in my own experience the following quote is more accurate:

Fartlek, which means "speed play" in Swedish, is a training method that blends continuous training with interval training. Fartlek runs are a very simple form of a long distance run. Fartlek training “is simply defined as periods of fast running intermixed with periods of slower running." For some people, this could be a mix of jogging and sprinting, but for beginners it could be walking with jogging sections added in when possible.

^{_{Source: Wikipedia}}

The idea is that as long as one does not stop it is a Fartlek. There is no strict structure, although one could impose a structure (e.g. sprint 100 meters, walk 100 meters, repeat) if one chooses. It could be just as valid to run as long as one is able, then walk or jog to recover.

To get back to your original example, we could restructure it a little bit to make it work around the noun Fartlek:

Shree made her way to the finish line after a Fartlek, completely exhausted and struggling for breath.