This achievement is easiest to get on The Devil; Specifically because the last reward for Apollyon's final encounter is a 100 Max Health card, as well as all of the equipment in the deck you might not already have.
Load up your deck with Max Life Encounters (Shrine, The Maiden, Alchemist, Man-Eating Plant, and Forgotten Dreams to re-play encounters) as well as Max Life Equipment (Lion's Heart, Imperial Armor/Helm, Ruby Ring, Shield of Aegle) and play through the Challenge like normal. When Theo asks for your Blessings on the second level, make sure to save Guardian Angel for the last encounter of the run.
Once you've gone through every encounter, make sure you have 200 Max Health before you reach the final Lord Apollyon, as well as completed all the elements to get Eternal Hope. If you kept Guardian Angel from the first level, and Ariadne for the card duplication, you have two 1/3 chances to hit the Huge Success. However, if you fail the Chance Cards, stop clicking through the encounter immediately and close the game, either through Task Manager or Steam's 'Exit' button. When you load back in, you'll be placed before the encounter, and can try again, saving you time getting through multiple run attempts.
Achievement Procs when you get the last 300 health: If you didn't manage to get 200 max health before the final encounter, you have a chance before the fight begins to swap your inventory. Equip all of the armor, make sure you have a one-handed sword out, and the two blessings you have should activate Ruby Ring. Drink up your Lion's Heart, and you should be able to make it even if you got unlucky.
As a side note, a lot of people have recommended doing this on Endless, but it often doesn't work for two reasons. The first is that any damage you take in battle, when your health is over 100, can deal Max Life damage, which can often make it difficult to keep your health up. Secondly, the encounters and rewards are much more random, and it's unlikely you'll be able to save up Max Life before you get hit in battle again, and go back down.