The last boss is in the final level of the game. To unlock the level you must complete level 11's required score and have 30 DNA. You will begin the battle dodging cannon balls that are falling from the sky. Once one lands that isn't red, push it into the cannon. Then the circular floor panels beneath you will open and spikes will come up. Kill the spikes before they go back under the panel. Then once he does his roar, get under a spike as arrows will cover the entire level except underneath those. Repeat this 4 more times and the achievement is yours.
Note: Each time you repeat he becomes more accurate and faster.