Tomb Raider

If you are boosting this you can make it go faster by winning by forfeit, so whoevers not winning just quit out when the game starts and the last player/s left will win the game (need to be atleast 4 players to start a match you can do this with one random but make sure hes on the winning team). This works both for free for all and team games. Theres still the problem with randoms but there arent really that many randoms playing anymore.

Credit also to liner bronson, ReagaStein and plesniaczek

You have to win at least one ranked match in each of the four multiplayer modes Rescue, Team Deathmatch, Cry for Help and Free for All. In the first three modes you play in a team, so after 2 or 3 matches your team should win eventually. A team match consists of at least two rounds and eventually a third round. Your team has to win two rounds to win the match.The tricky part is to win in the Free For All mode, because here you have to beat 3 to 7 other players depending on the number of players on the server. In Free for All there are three possibilities to win:
1st: You are the first player with 15 kills.
2nd: You are the player with the most kills after the time runs out.
3rd: You are the executioner and kill all remaining players. If a player quickly racks up kills, he/she becomes the executioner. You will see "executions remaining" on the left side of the screen. This is the number of kills the executioner has to get to win instantly. If a player gets killed by the executioner, he/she will not respawn until the executioner is killed. Executioners can win the round with around 9-11 kills only, but this requires some skills.

You can invite friends into a ranked match lobby, but because random dudes will quickly fill the lobby you will only be able to invite a few friends that can nevertheless help to boost by committing suicide (e.g. in Rescue), running in front of your shotgun or simply doing nothing. I suggest playing fair and if you are playing with friends better join the same side and play together. Boosting could be used for Free for All though, if you have to.

You can check which modes you have already won in a ranked match under "feats and setbacks" on the multiplayer screen. Press LB/RB and Right on the left stick to see the progress for all multiplayer achievements. If you get a draw (e.g. when you have the same number of kills in Free for All after timeout) you will not get credit for the win despite being number 1.

Edit: Please select "Find Match" and not "Quick Match" and make sure you are playing a ranked match.

Edit: Please let me know why you leave a negative vote. If you are not good in this game and want to release your anger, let me know. If you think I have not given enough information about how to win, let me know. I refuse to give game breaking advices like "camp at the respawn area" etc. because this achievement has to be done in public matches.

If you have problems, fill a lobby with boosting friends. If not everybody is able to join because the lobby is full, you can play a round and fill it again as some guys usually drop after every round.

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According to Gizmo2k you can get an easy win without much disturbance for other players. Be warned! Many users were not able to repeat this method successfully, but you should give it a try. Here is what Gizmo has written in the comments (in case you don't read those):
"Start a ranked match, as soon as the lobby countdown is finished and you see 'loading' pull out ethernet cable/turn off router WiFi, then turn it back on again. You won't be connected to Live, but you'll be in a match on your own and as long as you move about for the 10mins, you'll get the win. Reconnect to Live and win the team based ones, since they're so much easier to do and you'll get it timestamped, as opposed to a Ranked Achievement unlocking offline and looking a bit suspect ;)"
I cannot confirm this method, but it sounds legit as others have reported to get a win on empty maps after connection problems. Thanks, Gizmo2k!

Just ANOTHER edit: I am sorry for making this solution longer and longer. Gizmo2k's method has now been confirmed by many gamers, but it remains to be a bit tricky and cannot be repeated by everyone. You have to have a cable connection and best results can be achieved when you have a cable AND a WiFi connection. The cable has to be unplugged for a second either after the lobby countdown, the loading screen or even in the game. If you automatically disconnect from LIVE (which is not always happening), you should connect again (or you may be sent back to the main menu). All other players should be gone and you will get an instant win or you have to wait until the timer runs out (do not stand still for too long while waiting for the timer or you get removed). You should definitely check out the latest comments as there are huge differences in the timing of the disconnect and so on. Thanks for all the feedback!