This achievment wants you to be fast. It's best done on easy, as you don't have to rest to heal your heroes from injuries.
Don't rest, leave everywhere as fast as possible and skip time wasting additional events and restock on supplies before leaving.
Look random events up (here is a good guide with every outcome:
http://hubpages.com/games-hobbies/The-Banner-Saga-Walkthroug...) they happen in chapter 4 and 6.
Skip battles when you've the chance.
Don't waste a day waiting out at the end of chapter 2.
Leave ridgehold directly at the end of chapter 3.
Don't recruit Onef in chapter 4, as you can cut down the time that would be wasted with the optional event playing out in chapter 6 with him.
Don't search for scales at marek godstone in chapter 4.
Don't do anything on the bridge in chapter 5, leave Eintartorf.
In chapter 6, don't fight when you reach the fork, take the detour, after Sigrholm, pay the people to help you cross the water.
The achievement will pop, once you've reached Boersgard and you're allowed to enter the town.
Additional advise: As you're travelling fast, you can pair this achievement with
as long as you keep up your supplies.
You'll also don't fight that much, and as you'll skip Onef and the bridge in chapter 5 it woud be a good idea to also go for
The Innocent achievement in The Banner Saga worth 61 pointsAlette doesn't want to harm humans or varl...don't make her. , but you should at least be able to get