The serpent Cross on a tattoo is an often misinterpreted symbol that consists of a serpent being draped around either in a cross without the top, or traditional Christian cross.
Because of the twisting healical nature of the snake, many people quickly associated with the rod of asclepius the ancient symbol for medicine, or the caduceus the staff carried by Hermes trismegistus or Nehoushta the Brazen Serpent of the numbers 21/4 through 9 who is placed on a pole by Moses and was formerly worship by Israelites.

What does a cross serpent tattoo mean ?
Triumph of good over evil
This serpent cross is a symbol that was appropriated by the Christian faith to symbolize the triumph of the Cross symbolizing good over the serpent “evil”, therefore it is possible that the snake wrapped around the cross is also akin to the serpent described in Genesis, that had tempted Eve in the Garden of Eden.
Transformation of matter into spirit
However, typically serpents are symbols of wisdom. in fact for Gnostic Christians, the Serpent of Genesis was not a conniving evil figure but rather a hero of the Earth mythological story that convinced Eve to no longer be ignorant about her situation in the world and eat from the Tree of knowledge.
The serpent cross is said to represent the transformation of matter into spirit because a serpent slithers upwards towards Enlightenment rather than its usual position on its belly laying on the ground.

Alchemical indicator for the elixir of mercury.
The symbol has also an uncanny resemblance to the flamel cross, and alchemical symbol that was created by the famous Alchemyst Nicholas Flamel. that is why in regards to Alchemy, this symbol can be seen as an alchemical indicator for the elixir of mercury.
Within Alchemy, it was believe that mercury was an effective healing substance once toxins have been removed.
Alchemical interpretations appear to connect this symbol back to the rod of asclepius an ancient symbol for medicine back to Hermes also known to Romans as mercury and related to Medicine and back to Nehushta that Israelite minor God that was worshiped and fought against the toxins of snake bites.

However you want to look at it, despite it’s simplistic design the serpent cross is very interesting and old symbol that finds a home within the judeo Christian and alchemical mythologies.