Whilst 'finish a stage on 1 health' seems fairly easy, it is surprisingly annoying to unlock. Later in the game you usually end up healing after defeating monsters.

One way is to get enough damage reduction such that the first level deals 1 damage to you, but this requires either: an autoclicker, or patience to click shuffle 400 times.

Other ways recommend using the single serpent on level 2 (a damage reduction and HP up will technically work) but this is more often than not tedious, as if the enemy does a critical attack, the numbers are off.

An easier way:

1) Start a new save file.
2) Get up to Level 3.
3) Purchase 1 HP up (giving you 235HP) and 1 Damage Reduction (giving you -2 damage).
4) Battle the THIRD stage.
5) Take the first enemy down into 1-more-hit range. This usually takes 2 words.
6) Swap your tiles until he hits you down to any number ending in 1. For me, this was 201. Since he seems to have no damage variation, this should be a constant.
7) Defeat the first enemy and damage the second (ghost) to one-more-hit range.
8) Since the ghost hits for 12 (down to 10 with the upgrade), swapping your tiles will take you down to 1HP.

Enjoy the achievement. This should not take more than 1 go (2, if I am mistaken and the first enemy CAN deal different amounts of damage) and no more than 5 minutes.