After failing a couple of attempts on the first levels I actually earned this achievement naturally on the Queen of Plague Level.
You should have built a varied deck by now. Remove difficult encounter cards and insert cards that you earned from the easier levels. In Deck Builder pressing Y will tell you what the card gives, try to avoid cards which have combat written on them.
While luck has a lot to do with this achievement I honestly believe I earned it because of the deck I chose. If you use automatic deck builder the computer chooses the more difficult encounter cards, so make sure that you tinker with the deck and avoid inserting cards which have 3 failures to 1 success. Insert cards such as Maiden, Mr Lionel, Helpful Priest. Also remove cards which only have 1 chance of success and 2 failures.
There are also other tactics you can follow, find the quickest route to the exit, if you have the opportunity to flee, sneak or avoid encounters make sure you do. By adopting these tactics and manually creating your own deck you will earn this achievement in no time.
If you do enter into combat try and keep away from large groups, make sure you have a shield equipped and as soon as the counter icon appears make sure you counter. As soon as a red icon appears roll out of the way. By removing combat cards youll improve your chances though.