The "quickest" way to get to level 55 is to play private Wolf Pack games solo. I say solo as you will be more likely to rack up XP and complete the game quicker on your own.
You need to be aiming for about 1000 points per kill by always getting kills from a hidden position, waiting for the focus bar to show "150" and getting the perfect approach of 450 points. Your approach score is shown in the bottom right hand corner and you can wait for this to increase before killing your target.
You should also try and do as many of the optional objectives as possible as shown at the top left of the screen. Keep the aerial or acrobatic kills objectives until you get to the defend chests rounds and complete them then.
It takes 526,000 XP to get to level 55 and you'll get roughly 6500 XP per game leaving you needing to complete 80 games. With practice you should complete four an hour meaning this could take up to 20 hours to complete.
This will be shortened by XP awarded from in game challenges and an XP bonus you get for every consecutive day you log in and play a game in MP. I would also recommend purchasing a 25% XP boost pack from the Abstergo store. If you have the Freedom Cry DLC you get loads of in game currency for freeing 500 slaves so I used this to buy an XP boost.
Below is a video of me completing a game in just over 12 minutes to show you what I mean in practice.