I've heard that you can do it with some Thorn minions, or even by standing in the lava in the Tyrant mission - if you use Rest and some break frees 
@Golden Girl
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You could try getting a mission, popping a couple of purples and going into rest in front of an enemy. The trick is to find something that does resonable damage without killing you. I believe the damage must be to your base HP, so if you have HP accolades and such you'll need to make sure you're taking enough damage to sink below that. Because you're in a mission you wont be logged out for being afk - but remember to put yourself in hide so people don't waste time trying to ask for invites and such!
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I've heard that you can do it with some Thorn minions, or even by standing in the lava in the Tyrant mission - if you use Rest and some break frees
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Thanks GG dunno about the lava though since trollers regen cap is only 2000% at lvl 50 IIRC. But i could try since i have to go through maria jenkins to get my last 3 avs for portal jockey
One orange Guide (CoT) whilst on Rest should do it (especially if you have some kind of healing spamming power).
Rabbits & Hares:Blue (Mind/Emp Controller)Maroon (Rad/Thermal Corruptor)and one of each AT all at 50
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One orange Guide (CoT) whilst on Rest should do it (especially if you have some kind of healing spamming power).
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I think he's talking about his Ill/Storm, so no uninterruptable self heal.
As other people have said, find a CoT Radio Mission.
Clear everything except a single Guide (experiment with Guide level to find the best sweet spot).
Pop a couple of purples and then hit Rest.
Monitor for 5 mins to see if you set the Guide level too high.
Walk away from PC for a day or so.
Come back to either find a) your PC has locked solid due to a memory leak or b) a shiny new badge.
This is all just what I've gathered from reading various boards and guides (no pun intended), and I've never actually been arsed enough to farm for a damage badge, but there you go, that's the guts of it.
Warning:
The above post may contain Cynicism, sarcasm and/or pessimism. If you object to the quantities contained, then tough.
As a controller you don't even need to hit the purples before resting; just hold them. When they are released from the hold you are in full rest mode.
On my dominator I actually used a shivan in melee range. Worked a treat.
I got 4 of em but looking at the amount at the later made me realise that theres no way i could get those badges without farming them somehow. The question is though how?