You have to heal 10.000 times to get this achievement. This is probably the second last achievement you will get.
You can use the cleric or the engineer. Both count.
Healing yourself does NOT count.
Using healing circle does NOT count.
You have to use the regular healing skill. Try to get skills like Conserve AP and Shorter Cooldown.
You can check your progress. There are 3 badges.
You get one for healing 3.000 times and one for healing 6.000 times. The third badge is already for healing 10.000 times. But you do not get the achievement until the match has ended. If you disconnect before you have to redo your last heals.