Unlock 10 Character Heads or Skins.
Like said in the guide above, you can do it by simply playing a game and looting or by buying from Crazy Earl in Sanctuary using your hard earned Eridium.
Personally I would advice to just loot around and that way you should find it with ease before you even get to the half of story.
I would avoid spending Eridium because you will need quite a lot of it for
My Name Is Earl
trophy and you will be able to buy some nice weapons for it as well.
Don't forget to open/use them in your inventory. You don't have to wait with opening them till get all of them. Just use them as you get them to save space in your backpack as the game has no issues with registering them (at least in single player/solo mode).