I wouldn't suggest within a month, or even a year. The real pilots in wartime conditions even had a few years to accumulate that number.
It hopefuly would have a hefty reward for earning it. If it would likely take your average AH pilot, flying an average of 2-hours every day (or alternatively one or two days on the weekend), racking up an average of 10-kills an hour (a very generous rate), 261.15 days to earn that single achievement. If bombing 5 ammo bunkers is doable in ~30 minutes for 10-reputation points, then to scale the reward for an achievement that took 261 2-hour days to earn will/should/could be huuuge. Not that getting 5,223 kills in a F6F isn't already an awesome achievement in this game, but imagine if it got you 500 or even 1k reputation-points for it (or, alternatively, a unique star/symbol next to your name on the roster/buffer).
IMHO: I don't think there should be a lot of "big" achievements, but there shouldn't be a lot of "little" or easy achievements either. A good balance should have a few on both ends of the spectrum.