Do you want to get the praise or actually deserve it? Whaddya want, a medal? is a sarcastic thing to say to someone who is trying to get a compliment or praise for something they did. tossing in the "or a chest to pin it on" is saying "you don't deserve a medal, so which do you prefer, to be someone who deserves praise (has a chest, is manly and brave) or someone who gets praised even though they do not deserve it?
The idea here is that you want something you haven't earned, and they are being pretty open about what they think about you as a person, and it is not a good thought.