HammeredG 30

Deathfog Method

Undead Dwarf
All available attribute points into strength
One combat ability point in pyromancy and the other in polymorph
Learned the skills Haste (pyro) and Chameleon Cloak (poly)

I ran through the prologue until I got to second floor (setting your base class to any that would typically use a bow will give the evidence chest a high chance of having a bow that can be used to detonate the barrel easier when you get to it). Then, after getting the key, stood outside the door and casted Haste on myself. Opened the door and booked it to the barrels mashing A button. I got both but dropped one. Once in Fort Joy I ran up the ladder on the right side of where Dallis and them are. Got a little behind the two guards by the main doors and casted Chameleon Cloak. Used the toss item option to place the barrel as close to Alexander I could and shot the barrel instantly.

This took less than 5 minutes...most of that being load times.
Hope that helps!