Is it possible? And if it is, what's the quickest way to get all three classes?

It is possible. Go straight fighter first, putting your skills (cross class) into Intimidate and Hide while picking up the requisite feats.

You should only need 7 levels of Weapon Master and about 6 levels in Fighter. Place the rest in Blackguard.

Unfortunately, this spreads your stats quite thinly since you need Strength, Dexterity, Intelligence and Charisma. You cannot afford to neglect Constitution as well since you're a frontliner and Wisdom is needed for saving throws. Your character will not be very powerful, but it is possible.

I see little point in this build powerwise, but good luck with roleplaying your dark weaponmaster!