Eye of the Storm Veteran
Win 100 times. You know the drill. This is easier than accumulating other victories because Eye of the Storm matches never last for very long because points tick for every second. The more towers a team controls, the more points per tick and the more each flag capture is worth. Even if you lose a game, it's never such an excruciating wait.
The Perfect Storm
Win 2000-0. Anybody who has played Eye of the Storm enough times will know that this happens rather often, more so than Arathi Basin, at least. This is because unlike Arathi Basin, towers are controlled through numbers and proximity, so overloading a tower will lead to its conversion. As long as a team starts strong or in greater numbers, it will usually result in control of the towers nearest the opponents, which sometimes results in a 4-0 game. It's easier from there. Play enough games to reach 100 wins, and you'll pick this up along the way.
Eye of the Storm Domination
Win 10 times while holding 4 bases. Again, along the way to 100 wins, you should encounter enough games where your side controls four bases. In fact, holding four bases usually results in wins, anyway, so winning under these conditions typically go hand-in-hand. This won't require much effort on your part. Just hope the rest of your teammates know how to play.
Win in 6 minutes. Finally, an Achievement that's slightly harder to accomplish solo. Fortunately, Eye of the Storm is a Battleground where starting with a bigger force usually results in a quick win. One of the matches in your Eye of the Storm Domination should be a six minutes or less kind of game. Not as effortless as the other Achievements so far, but nothing too difficult, either.
Kill 5 flag carriers. Here's another moderately difficult one. Most of the time, the team that has a distinct advantage in tower control only needs to capture the flag a few times. This means fewer opportunities to kill a flag carrier. The good news is, once a flag is dropped, another player can pick it up. In theory, you can let enemy players pick it up over and over, and you can keep killing them. Still not an easy thing to orchestrate.
Capture the flag. Just how easy is it to get Master of Eye of the Storm? So easy that one of the primary requirements is to... capture a flag. It's so ridiculously easy it doesn't even require you to do it fifty times like in other Battlegrounds, or be creative like capture a flag to score the winning points. Piece of cake.
Bound for Glory
Capture the flag 3 times without dying. Now, out of all the Achievements in Eye of the Storm, this just might be the honest-to-goodness difficult one. Even then it's nothing compared to other Battleground Achievements. The real problem with this is that once you cap the flag, it will respawn a few seconds after, making it impossible for you to be at the middle in time to get the next one. This means either the opponent or another teammate will get it. If you're dominating a match, such as holding four towers, you can only capture the flag no more than three times (each flag capture is worth 500 points if you control all four towers). Oh, and you shouldn't die until after you've captured three flags -- not before the first capture, at least. You can die as many times as you want to after the Achievement.
Get a Killing Blow while under the effects of the Berserker buff. That's it? Seriously, Blizzard seems to have run out of ideas when they designed this meta-Achievement because this Achievement is a joke. You see a Berserker buff, you grab it, you kill. You essentially need to make one killing blow in about a minute. That's a long time in PvP.
This is the easiest Battleground mastery of all to pursue. It's even easier because Eye of the Storm is a lot of fun, it's very dynamic, and never lasts longer than it should. There's a lot of combat to take part in, and because towers are captured through numbers, you'll always be in the company of a group (hopefully). However, there are other Achievements that aren't part of the meta-Achievement which in all honesty I can't figure out why they weren't included. Anyway, since you're in there, you might as well grab a few other Achievements.
Capture a flag while your team holds four bases. Why isn't this part of the meta-Achievement? I don't know. But this isn't as hard as it looks, although considering one flag capture when your team holds all four bases is worth 500 points, only a few players will be able to do this per game. It's challenging enough, but if your team holds all four bases, it likely also means you control the center. So your biggest competition here, really, are fellow teammates.
Kill 5 players at each node in one game. Again, this isn't part of the meta-Achievement even though it's nearly identical to Arathi Basin Assassin, which is part of the Arathi Basin meta. This is doable as long as you stick to a roving group. The only thing that makes this difficult is if your opponents don't cooperate and don't assault a node through the entire game. It happens often enough that you can be roving and miss the action.
Take a Chill Pill
Kill a player who has the Berserker buff. This is the opposite of Bloodthirsty Berserker, but is slightly more difficult because you have to chance upon a player who has it. You can theoretically camp the Berserker buff, but it spawns randomly in towers so it's not as sure a thing such as in Warsong Gulch. Not a part of the meta-Achievement, even though it's considerably easier than Storm Capper.