The merchant achievement is awarded when you successfully complete trades with 50 different players.
Master Merchant Achievement
Trade with 250 different players.
You can only trade on either market worlds or private worlds. Trades made in both market worlds and private worlds count towards this achievement.
Since it doesn't matter what items you trade, players sometimes get this achievement more quickly by finding others who need the achievement and then simply trading one earth for one earth.
Sometimes, if you go to a market world and simply announce that you're trying to get the merchant achievement, helpful players who already have the achievement will agree to trade earth to help you out. Don't count on it, though -- markets can sometimes be rather hostile environments.
Merely initiating a trade doesn't count; you must actually successfully complete each trade.
You can't get this achievement by trading over and over with the same player -- you must trade with a different person each time for it to count.