“You can sling Bull with the best of them.”— In-game description
Expert Excrement Expeditor is a Fallout 2 special perk, which means that it can only be gained during gameplay, not by leveling up.
You can gain it from shoveling brahmin dung for Bill in Broken Hills five times in a row. You have to have at least 4 Intelligence to get this perk, as otherwise you only get to shovel dung once.