If you go to the PROFILE link at the top of the page, then select AWARDS and SHOW AWARDS you will see the badge list. There should be a decent set of instructions telling you how to get each one.
It doesn't have to be solo carry, and you absolutely can try to obtain multiple badges at a time, just be sure they are simple enough for one of our overworked moderators to verify easily enough- ie, don't post something in the middle of a 700 post thread, then link to the first page and say "it's in there."
The more badges, the merrier!
Def