This achievement can easily be obtained by playing as a Medic and taking both the Heal Beacons and the Medical Gun. Note that both are required to get the achievement, as the medical gun alone cannot heal sufficiently before running out of ammunition. This makes it impossible for you to deal any non-melee damage unless you switch weapons during the mission. Unfortunately, you will have little offensive capability and should exercise caution in firefights.
If you do pick the above method, consider equipping the Power Fist so you can fend off aliens that reach you.
Make sure you stay nearby your teammates so they can protect you, but not get in the way of them so they won't Friendly Fire you.