When I joined a league going after the Keyes badges, we specifically trained for the Green Stuff badge. The league leader had an AoE power that froze the ground that he colored green and even designed a costume similar to Dr Keyes'. Even so, it tooks us about a dozen attempts over a few days to get it.
You can FARM the Empath badge by getting the Rebirth Total Core Invocation (T3 is fine) and then travelling to Mercy Island. Near the P2W agent is a large group of stationary Arachnos soldiers that you can auto-fire while afk. It took me about 3 nights or so for my Blaster (!?) to get the Empath badge. Great conversation piece! Lol!
Someone showed me a way to farm damage taken in the Maria Jenkins arc. There's a lava pool in the last mission. SOMEHOW, they told me to get into a Rest position and then slide into the pool. I did this and was being damaged at 91/sec or so. The next day I tried to do it again, but I couldn't stay in a Rest position and enter the pool. I never found the person again to figure out how they did that.