Expedition challenge not recording my hiking activities

It should just be counting your steps. Are you seeing these recorded on your watch?

My Forerunner 220 does not record steps but it does show elevation ascent when I record my activity as a walk. Once i change the activity to a hike the ascent stat disappears.

Ah. You are someone who has determined that a hike is not a walk. Don't worry, you are not alone

Personally, I use the two words as being interchangeable so I'd leave it as a Walk, but I know that doesn't speak for everybody. 

You could try leaving a suggestion at https://www.garmin.com/en-GB/forms/ideas/

to get hikes included.

Runner521 said:

My Forerunner 220 does not record steps but it does show elevation ascent when I record my activity as a walk. Once i change the activity to a hike the ascent stat disappears.

For the expeditions, the activity type does not matter. In fact you do not have to record any activity at all. And the elevation profile in the activity is also unimportant. You just need steps for the distance expedition challenges, and elevation from the barometric altimeter of the elevation expeditions. Forerunner 220 does not have any barometric altimeter. It logs the elevation using the GPS, and that does not work for the challenges.

In other words, unfortunately, with your device you can get neither the distance nor the elevation expedition badges.