Does losing soul heart count as actual damage? [duplicate]

Solution 1:

Yes, losing soul heart counts an actual damage.

No Damage Achievement Guide says this about damage:

What counts as "taking damage?"

• Getting hit by an enemy, enemy projectile, bomb
• Purchasing an item from the Devil Room.
• Spike door in the Curse Room.

Also, No Damage achievements are awarded only for some parts of the game, there is no special award for completing entire game that way:

Basement Boy, Spelunker Boy, Dark Boy, and Mamas Boy. They are unlocked by completing The Basement, The Caves, The Depths, or The Womb without taking damage, respectively. There is no achievement for completing Sheol, the Cathedral or The Chest this way.

Solution 2:

From the fandom guide:

What counts as "taking damage?"

• Getting hit by an enemy, enemy projectile, bomb

• Purchasing an item from the Devil Room.

• Spike door in the Curse Room.

What doesn't count as "taking damage?"

• Damage that is absorbed by shields, e.g. Holy Mantle or Infamy.

• Using the Blood Donation Machine or IV bag.

• Damage taken from the Devil Beggar.

• The "Bad Trip" or the "Health Down" pill effects.

• The Razor Blade and Blood Rights items.

• Using a "Health up!" pill.

As you can see, if you get damaged even if you have soul hearts, the achievment will not be accomplished.