To exchange items with another player you must be in the online lobbies.
Once in the lobby you will be given the option to "Hand over item" with a player by using the X button, once you hand over an item to a player all that player needs to to is hand you over an item in return and you'll earn the achievement.
This shouldn't be too hard to earn but you can also just do this with a party of friends if need be.
If you vote down please tell me why and ill do my best to correct the solution.