You will need a health pack (looks like a bag) to heal a team mate.
While you can find the health packs throughout the game, the easiest way to get one is to buy from the safe room at the start of a run. It costs 250, but you start the run with enough to buy one.
While the bag can be used on any teammate at any time, you can ONLY unlock this achievement if you actually heal them. So don't use the bag in the safe room. Wait until you are in the thick of the action and the player you are healing is taking damage. Pay attention to the health bars in the bottom left of the screen
When they are taking damage, run up to them and take the health pack out. If you have no other items equipped, it will be the
button.
While standing them press
and wait for the progress bar to complete.
The achievement won't pop right away. You will have to wait until the end of the run and head back to the hub area. It will pop then. The same for MANY achievements in this game.