I've completed all the projects requiring building skills (statue, all huts, and clearing the rubble and leaves), but I haven't achieved the jack of all trades award yet. All of my villagers with enough building skill to attempt the award are too old to actually max them out on other skills. I know you can repair huts to gain building skills, but can you gain enough to become a master builder?

Also, does the bar need to be completely filled, or does the villager just have to have the master builder tagline?

You can gain enough to become a master builder and it only requires a master to get jack of all trades

Your best chance to succeed at this challenge is to start with a "runner" at 14 years old.

Since you have already completed all the building projects, you will constantly have to drop him/her on huts to repair. Be very diligent, and if possible pay attention only to this villager. It also helps to pause the game when you aren't playing.

Once this villager becomes a master builder you should move to farming, then research, then healing. I would save parenting till last.