Titanfall

Please refer to to see how to join ranked play.

When you play with your rank chip on, you earn battlemarks. The way to earn battlemarks is listed on the Ranked Play page, but essentially involves doing whatever objective the gametype entails. Any deaths will detract from the score to earn battlemarks. As noted in the other guide, unless there are enough players in the lobby the chip isn't activated. I haven't played in a long time, so I'm not sure how many are actually required.

Deaths barely detract at all, so I'd say just play your best gametype and you'll earn this in no time.

Last Titan Standing may be the easiest gametype as the only thing relevent to battlemarks is doing damage to the enemy titans. As far as the list says, deaths don't matter, but I'm not sure if that's true.
You can earn up to 5 marks a game.
Since each Bronze rank requires 5 marks, and each Silver rank requires 6, you will have this by the time you are Gold.

As Foxy noted in the comments, once you have locked in a mark (IE there is a green symbol in the bottom left of the screen) you can not lose that mark, but you can lose progress towards the next mark.

Credit to dc0dr - You don't need to earn 50 in 1 'season', you just need to earn 50 total.

UPDATE - Battlemark loss now works slightly different. I don't think losing a battlemark subtracts from the achievement but figured I'd mention it.

As of November 6th - If you earn 75% of a battlemark, you won't lose a battlemark when the game ends.
As a result, however, they've made it so battlemarks don't crack anymore. So if you don't get at least 75% of a battlemark, you'll lose one. Since you only need 50 marks this shouldn't be a problem.