Probably 7-10ish. There's a lot of story-time and even though I had almost no S-Links to pursue, I went to the Arcade 1-2 times every day to pump up my default every-situation Persona(Titania for life yo.) You also have a five boss Block 6 to cleave through. My last few hours were spend 1 hour losing to last boss, spend 2 hours gaining 5 levels, spend 1 hour winning game. Everything else was pretty matter-of-fact and leveling as I went.
The grinding isn't insane unless you've somehow squeezed through Tartarus.
In example: The 12th Shadow in October is Level 56. The Last Boss in January is Level 76. I always go to the limit of Tartarus the instant another block is open. I got to the top of Block 5 about 40 days in advance. I got to the top of Block 6(ready to beat the game) with 17 days to spare.
I got my ass kicked in the very last phase of the last boss at level 71.
I spent 2 hours getting to level 76 and thoroughly kicked the fucker's ass, although I also made sure to stack my HP to prevent the chance of accidental wipe. I died the first time at 71 due to a Critical + an AoE attack follow up.
So I used a crafted Balmung (+100 HP) and a +30% HP Ring(you can buy 'em at the mall halfway through the year, I've used them on every character since.)
Grinding is actually pretty painless in Persona 3 if you get good at it. Always get First or Neutral Strike, have a Persona with group elemental attacks. My most-used Persona was Titania, a level 45ish Queen of the Fairies. She learned Magarula and Mabufula and fused with Mazio. My last two levels were just dumping Mazio + All Out Attack on quartets of Lightning-Weak Final Dice. Obviously you want to win wands at the shuffle. I also compulsively save between levels, before and after every block boss, etc.
The last boss is cool but kinda boring due to the constraints of partner AI. At level 75, Yukari learns a party FULL HEAL, but even if set to Heal/Support, she favors using single target Full Heal to patch you up. So I spent most of the fight with Titania and her Mediarama shooting out 370 HP to my entire party every round. If every single party member got knocked to 40% health, Yukari's AI might wake up and cast the party full heal and give me a blessed chance to attack.
[spoiler]In the last phase of the last boss, I was using Koro, Akihiko and Yukari set to "Act Freely." This caused them to favor casting their best elemental attack. This was useful because their AI can't handle the Last Boss's "Moonless Gown", a permanent reflect effect. But they'd just cast their element, bounce it back to themselves and take no damage. If they actually hit it via "Conserve SP", they'll take 500 damage per reflect. Once you can change their AI, set it to "Heal/Support". At level 75, Koro would just give the party +Evasion/Hit and Akihiko would debuff the boss with -Defense and then -Attack. This also causes the Boss AI to break, in that he always attacks twice, but he always prioritizes debuffing. So he'd often give me a break during or after Moonless Gown phases.. like, "Cast Moonless Gown" + Group Attack, Rebuff Self + Debuff Party, "Uncast Moonless Gown", Rebuff Self, I reset my partner AI so that they hit the guy. My Titania could throw out a -Evasion to the boss or I'd use a +Defense Sutra to soften up the Group Damage from the boss and increase the odds I'd be allowed to attack.
At the last quarter of the last phase, he begins spamming an AoE with a chance for random debuffs. Your healer(my Yukari) should be set to Heal/Support permanently at this point and you just need to let your attackers slowly bring it home while not letting things get crazy.
No joke that it's an hour long boss fight and that's if you're killing him as fast as possible. You WILL need Somas to keep your entire party from running out of SP and to prevent the boss from killing you during a down-time. At least three of them.[/spoiler]