The first thing to say is that the badge system hasn't been updating for ages. (I've reported it lots of times and the Ed has promised to get it fixed but nothing has happened!). So your collection of badges might currently be incomplete.
To view
which badges you've got, simply click on the 'Badges' tab in 'My Profile'. To see all available badges, see here:
http://www.theanswerbank.co.uk/badges/