In addition to the information that has been posted. You need to be a minimum level requirement of 90. Thats just to be able to do the required difficulty of this. The best place for you to level up has been and is still White Beast on Neudaiz.
It takes 6.7 million exp to get to 90 alone. I have lvled 8 characters to lvl 90 minimum and I can tell you that 1-100 is possible in a month with event experience. But not without. Considering no one has even thought of trying to put this together for the achievement hunters, here's a little bit of math for you, then you can review that with all of the experience gains from enemies and bosses and such on psupedia.info.
It takes 6.7million exp to hit 90.
You have 31 days in a PSU subscription, 31 days X 24 hours a day = 744 hours.
If you played for 24 hours a day for 31 days you would need...
6,7000,000 divided by 744 is 9,005 per hour
That dosent sound like that much except for the fact that you would have to average that much exp if you played literally 24/7 without eat sleep or breaks.. Even if you played 12 hours a day, you would need to average 18k experience an hour. So take that and actually see how much you gain in an hour. I guarentee in the first 3 days you will be in your 50's then it will slow down alot. I know, I've been there. Also Halfway to lvl 90 experience wise is lvl 75. I'm trying to be truthful with the lack of knowledge on how this can be done. Realistically How many hours a day every day could you put aside for this game? Aside from Work/School/Real life? Heck many people will play some other games along the way too, because they may be bored with PSU.
Say you play for 5 hours a night, every day for 31 days. You would have to average 43,225 exp per hour to make it to your lvl 90 goal. Check the experience charts on psupedia.info, 100K+ in total on character experience is in the low lvl 20's. You need to get 20 lvls in 2 hours, anything less and your going to be behind. And considering your lucky if you get 2k experience from a boss fight from C Rank and some B rank missions, which is pretty much all you do in the 20-30 lvl's
But experience gets better in higher lvl missions! Yes well as you lvl up so does your experience requirement. Again check out the experience charts.
Add to the fact of not having someone 100+ boost you the entire way, random parties not working out, or even getting booted for random reasons, your going to have a hard time if your new to the PSU community and want to get anywhere fast.
I'd really like to see someone set an active "goal" on doing this, Theres so many different things that can happen online this really is a game of chance, For example you happen to land 3 rare missions in a row, thus gaining huge amounts of exp, Or stumbling across a really expensive item you don't need, Selling it and gaining a lot of meseta to better your pallet of weapons.
Saying you only have to get to lvl 90 to get the achievement is just the bare minimum.