How to get the Healing badges

The 'legal' way
Well, heal anything that's taking damage. In Siren's call there's always fights among the NPCs and you can practically win the zone with a decent AoE heal power, healing all the NPCs. Play in big teams, participate in events with big crowds (hunting the RV sig Heroes usually gives a lot of healing for me)

The slightly evil way
Get into a mission with a friend that wants the damage badges. Target him/her and put your single heal power on auto from a pretty far distance. Make sure he 'Rests' while he takes damage (see the damage guide) or not, if you wanna get som über-healing. You could of course also get a second account and use 2 computers for this.

The evil MM way
Get one of your low level pets to take damage, use the healing power you have to heal it. If you don't have a heal power, you might concider the power pool's heal other. Apparently if your pet has a healing power, any healing it does will not count, only the healing you do! But you can also give insps to your pets and a heal insp seem to count... so far! Try giving insp to the heavy in RV! :)

The really evil way (requires disruptor and the Longbow Warden 2 gladiator and a friend)
Setting this up can be a real pain, but it's worth every second, and it's quite spectacular too.

Get a friend to join you in an arena pet fight. Let your friend make the pets fight eachother 1-on-1. Unless your friend also has a healer gladiator, you shouldn't let your pet attack his - put them on passive/stay.

Make them stand close to eachother so the warden can use his AoE heal too. You should have one expensive pet that does a lot of AoE damage. Villains can use the Slag.

Target your friend and let the warden 'attack' him. That way the warden do no damage, he'll just heal constantly.

Getting the Longbow 2 gladiator is a pain, but you can get it as soon as you can get to the PvP Zones. Once you've got it, the arena can be set to a high level fight, making the warden heal a lot. For some real über-healing you should try setting up a team pet fight with 3 buddies. that way you'll get more minions for the wardens to heal, but it's even more annoying to set up and if just one of you DCs it's bad, bad, bad. Also: The devs really, really want to get rid of this, but haven't found a good way yet! :)