Looking at that list of multiplayer achievements and based on my own personal experience online, the majority of them will be very easy to get through regular play. Here's some tips on getting some of the trickier ones.
Mastering the Art:
Earn the INCOGNITO bonus (Multiplayer).
You need to get an incognito kill. Depending on your skill level, this could be a tough one to get. To get an incognito kill, you must fill up your approach meter to the max by keeping your target within your line of sight without running up to it or otherwise making yourself noticeable. Note that you can run without reducing the meter if they are not within your line of sight.
Make the Headlines/Tactician:
Obtain 12 different Accolades (Multiplayer).
Score at least 2500 points in a session (Multiplayer).
To be successful in multiplayer, you need to always go for the quality kills. You won't necessarily win by getting the most kills, you win by getting the most points and kills only grant you 100 points. If you are more patient, you can get bonuses to earn you even more points. Being fast an efficient will get you this achievement naturally.
This could be tough getting because you will need to be quick at getting your quality kills while still fending off pursuers. I can't really help much with this, you just gotta be a machine and some other players can be very difficult to beat. Though out of all the game types, Deathmatch might be the easiest to get it in as everyone is in a confined space and there aren't (normally) any lookalikes so should be easier to find your targets.
The other achievements you should be able to naturally earn if you go after the True Templar achievement of level 20. Depending on your skill, it might take a couple of days or so of playing. You shouldn't strain yourself over this too much if you plan on playing a lot.