This achievement is easy to obtain on the first boss: The Golem. He is located at the end of the first jungle world.
*UPDATE* Credit goes to DamTheLad for pointing this out. You can obtain this in either story mode or Arcade mode. Thanks for verifying that!
Begin by standing just outside the reach of his hammer arm. He will pound it into the ground, releasing a wave that can harm you. If you are standing close to him you can immediately jump over this wave and onto the hammer. Jump again to the upper level of the hammer and slice at him with your sword. If you get there right away you can get 10-12 hits. Watch out for the wave though, it will travel back to the hammer and up to where you are standing. Jump away back to the ground. Repeat this again for the second wave. If you have timed it well he should be two thirds (or slightly more) dead. After you complete the second set of attacks and jump off to avoid the wave, watch out for the 4 hanging enemies. They will fall to the ground. Kill them quickly before the colored lines fall from the sky. You can let the blue lines hit you, but avoid the red ones. This is over after about 30-45 seconds. Then, when the Golem's hammer hits the ground again, jump over the wave and onto the hammer for your third round of attacks. If you have timed the first two well then this set will kill him. If not be prepared to dodge more falling enemies and colored lines from the sky. The achievement will pop as soon as you strike the final blow.
If you get hit then exit the game from the main menu. When you reload the game you will begin at the start of the boss battle.