There are a few methods to manipulate getting to one life.
If you are starting this game fresh on a new save AlbinoKidElite has helpfully pointed out you can play through levels one and two
then start level three
without any upgrades.
Make sure you kill the first enemy only taking one hit for 19 damage, ignore the shopkeeper then get the second enemy weak and keep swapping tiles (
) until you drop to one life, then finish off the enemy and then the level.
If you've already played Letter Quest for a bit,
depending on how much you've already played you can get the first health upgrade and damage reduction of 6.
If you are already past this point buy all the upgrades for damage reduction to reduce damage taken by 10,
(you can also get the upgrade to see how much damage you will deal to an enemy to be on the safe side not necessary though).
Then go into the first level and weaken the enemy to within one hit.
Now the boring part, just keep pressing
to reshuffle the board this will also work towards
Doing this causes the enemy to attack each time dealing damage taking you down to 1 health eventually.
Lastly an important note make sure you haven't got any form of life gain equipped whether it's a scythe, or one of the books, because the last thing you want is to get down to the magic one life and then kill the guy and get life back missing the achievement.
Also as ProjectSix points out avoid orange crystals as this will also regain life.
One last suggestion is that it may be quicker to get this in a new save file where you can start from fresh and follow the method at the top with a new unupgraded character.
If anyone has any extra tips comment and I will add them in.