Just to avoid confusion as Ive seen a lot of people on other forums talk about "beat the game twice in one sitting" and thats not true.
To get this achievement you just have to beat New Game +. This is unlocked by beating the game once.
Depending on how long you spent in the normal game NG+ could be very easy. I beat NG at level 120 so I was pretty powerful by the time I went into NG+. A few big runs to get gold and I have more than enough power to defeat all 5 bosses.
If your struggling though you can use the Grace Runes. These send the enemies back one game type, so if you are in NG+ all the enemy types will revert back to NG. I wouldnt recommend completing the game like this because it wont help you when it comes to the other achievements but it will help you get a few big gold runs if you need to improve your stats.