Yes it is possible. A few things need to be clarified.
1. You need to be treated with a q-switch laser (Alex, Ruby or Nd-yag).
2. You will require multiple treatments
3. On a few occasions, there is a paradoxical darkening that occurs with the colour of the tattoo, depending on the colour, especially if it is red. This would then require many regular treatments to get through this phase. No guarantee can be given, though, that the colour will lighten or go away completely.
4. The treatment is fast and often done with a numbing cream only, although an anesthetic can be injected to make it less uncomfortable depending on your symptoms.