Note; The LOTR: Battle For Middle Earth 2 servers have now been closed and this achievement is unobtainable!Now for this achievement, like it says in the achievement description you need to lose a game to someone ranked at least 20 places below you and due to the recent leaderboard reset this achievement is easy enough to get, now due to the game being pretty much dead online you'll need to find yourself a boosting partner, if you don't already have one you can create a session and hope to find one here;
http://bit.ly/fIcgpfOnce you and your boosting partner are ready, select Xbox Live from the main menu and then ranked match, now you need to choose a game type, I recommend you go for this on the "Versus" leaderboards, it seems to be the leaderboard with the most players on which will make you able to jump up the leaderboard a little easier.
So one of you create the game and the other search for it, the nice thing about matchmaking on this game is even if someone else joins your game it doesn't automatically start up, so you can quit out and create a new game, but in all honesty you shouldn't have much trouble when trying to pair up.
When you're in game have the person who is ranking up first literally do nothing, the person who is losing should select his base by pressing "A" on it then holding "RT", use the D-pad to move the cursor over until you've selected the option to demolish your base, press "A" on that and you'll lose the game, repeat this process a few times and then you'll have to wait as the leaderboards update once an hour, keep checking back and once they've update repeat the process again but the person who was previously winning will now be the player who is demolishing their base, upon losing your first game you'll get the achievement, all that's left to do now is help your boosting partner get his achievement, you can also use this method to get;
Solution for The Hobbit and the Troll In The Lord of the Rings: The Battle for Middle-earth II, if you don't have it already you'll get the achievement while using this method so long as you boost your rank up enough, how many games you decide to do is up to you but 10 games should be more than enough.
Just to clarify, while trading off these achievements using this method, the person who is ranked high will get; "Try a tutorial" when they lose to the lower ranked player, at the same time as this, the lower ranked player will get; "The Hobbit and the Troll" when they win the game (beating the higher ranked player to get them the "Try a tutorial" achievement), I hope that clears it up.
This method will take you a little over 2 hours due to the leaderboards updating hourly.