The first part of getting this achievement is simply starting a HUT team. That's pretty straightforward and will be done for you once you select Hockey Ultimate Team from the main menu. Once you're team is ready, choose play game and then tournament. There are online and offline tournaments available, make sure you select an online tournament by using the L/R triggers to find them. From there, it becomes dumb luck. Win four games in a row without someone quitting on you and it's yours.
Winning these things legitimately takes time, effort and dedication. The best way to build your team is to play offline for awhile first. Use the players you get in your intro pack to win a few low level, offline tournaments and build up a collection of pucks as you go. Use those to buy Peewee packs. Any rare or exceptional players you get should be saved for the time being. Once your team starts looking a little bit more like an NHL team, players averaging in the 80's, you can try your luck online.
Luckily, you can actually boost this achievement with a friend. Party up and choose a tournament. Coordinate so that you're both searching for an opponent at the same time and you should match up together. If you don't find each other, you can back out of any game you get matched up in. It's best to do this at off times, like the morning or afternoon on a weekday, to make the searching process a little easier. Simply beat your friend, who should be pulling his goalie for you to score an easy goal or two, and repeat the process four times.
To make the time go faster, try not to play too much. Every stoppage of play adds about 10 seconds to the game which can really add up over time. Take possession of the puck and skate behind the opponents net. Your friend should take control of the defenseman who pressures down low and you should be able to sit still for the entirety of the period. This greatly reduces the amount of time the games take.
Cheers!