The answer will vary a lot depending on how much gold you have saved up. For someone starting out completely from zero, my guess is maybe around 200 hours.
Maybe someone has a more precise answer; I didn't really keep track of these things when I was filling my hall.
if you have 2 plat but are in a core doasc team, no time at all. if you have 2 plat and no farming or SC experience, more. if you go for the right titles/pets/armours and get lucky with sellers it will be quicker than if you go for legendary skill hunter and carto and cant find a good seller for minis. also, 3 months could be 100 hours or 1000, so its a wide timeframe.
my advice is just play, and then fill hom one point at a time, it will still eb full in 6 montsh if your not awful, and your less likley to get bored of grinding titles
Someone gave you a timeline, around 200hours. I'd say between 200 and 300. Wether or not you can fit that in 3months is entirely yours to decide, since you haven't said how much you plan to play. You could do it in 2weeks if you played a lot, and it'd be very possible. Check the Community Works forums it has threads on how to get HoM, how much it will costs you and what to do to get there.