There is an, achievement of taking nine hearts damage at once. I have been trying to complete it for almost a month still every time I try the player dies or I take 8 1/2 hearts of damage. How many blocks should I fall to take damage, or is there any other way to complete the achievement?
I think you're misunderstanding the objective of the achievement. This is the achievement:
Overkill: Deal nine hearts of damage in a single hit.
This means that in a single swipe of your sword, or a punch of your fist, you need to be able to deal nine hearts or more damage to an entity you're attacking. This is accomplished through enchantments and/or status effects.
You misunderstood the achievement as taking 9 hearts damage to yourself, when the achievement is for dealing 9 hearts damage to other mobs.