No tattoos cannot be removed in one session. The colour, the amount of ink and the depth/layer of tattoo used determines how fast tattoos can be removed. Your body clearance and the ability to heal or risk of getting hypertrophic scarring certainly plays a part in tattoo removal.
The reason why it needs multiple sessions is because of increased risk of scarring with each increased power. A experienced doctor will know how to determine what power to use to manage tattoo removal with the power used.
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Related: The Ultimate Guide to Tattoo Removal in Singapore