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The Lost Planet 2 Crown, seen in game as the LP 2 Crown is unlocked by being in the Top 20 in any Online Multiplayer Leaderboard in the game. Upon unlocking the Crown you are greeted with the following message.
"You have shown the world what you are worth by reaching the top of the leaderboards. As a reward, you can now wear the LP2 crown that will identify you as a titan among titans.
But beware! You can only wear the LP2 crown as long as you maintain your rank on the leaderboards!"