You start a round with a full five hearts. This gives you 4 hearts you can lose to damage before dying. That means you must find another 4 hearts through an act, collect them while missing one or more hearts, then get additional damage to bring it up to 8 total lost hearts before crossing the finish line of the scene. You *MUST* complete the scene to obtain the achievement.
Additionally, by ending the stage with only one heart, you will also obtain the following:
Act 1, Scene 1 is good enough. There are several points where you can gain a heart in the middle of the scene, with each 'switch' of the layout being a part of that scene:
1) Part #3
2) Part #7
3) Part #10
4) Part #11
5) Part #12