You will start a new game with 7 max health. Later, you can raise it to 10 with the skills 'Oak Skin' (+1) and 'Resilient' (+2).
This means that you will need to find items and blood blessings to boost a further +10 during a run. Greed sells various +1 and +2 buffs, so look for those. I was able to get this achievement by getting my max HP above 15 then finding the blood blessing to raise it by 33%.
This will probably come during natural play, but may take some luck so just keep trying!