I found an excellent video walkthrough on youtube that helped me complete this challenge. There are a few rooms here and there that require a bit of luck to pull off the same stategy used in the video but they are doable with some patience.
As for the Baron fight, practice makes perfect. A good strategy is to hang around the desk that you can break in half. Also, try to make quick work of the pirate zombies that appear in the last wave before they start hurling treasure chests at you, and definitely keep your distance.
All credit for the video goes to the original uploader, RarewareArchives.