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You'll have to get to level 60, three times, one time with each faction. It will take at least 50 hours for each, strongly depending on your skills. However, being a medic and completing as many objectives as possible is a great way to level up quickly. Use and overuse FRAGO bonuses to give you more XP, and if there's a double XP weekend, play in it to have a real boost.

Since 1.07, some modes will give XP bonus and you get double xp when playing for your first hour of the day.

Since 2.00, even if you get your trophy at level 60, you need to go to level 70 to use the Veteran mode and change factions. You'll need around 110,000 xp to get to level 70. This works like Prestige in Call of Duty: you lose all your skill points and your skills, you restart to level 1 but with a special insignia and you get a permanent 10% XP bonus. You also keep all your stats (so you can go into Veteran without losing any medals or ribbons) and your command experience. However the game chooses the Squad Leaders, the Platoon Leaders and the OICs depending on their level so you'll need to level up a bit to be a leader again.

Since 2.10 update, you can use the Multiqueue feature to get a good xp bonus. The more modes you choose, the bigger your xp bonus is.

You can also use the two additional slots to create soldiers from other factions but it will cost you $0.99/month.