Unlocking the quest
You can unlock this quest in Beauclair. Go to the main market (M4,19) during day. Geralt can encounter a painter there and then agree to pose to a portrait.
Follow the painter
You must meet with painter again at noon - he will be waiting near the Palace in Beauclair. Jump on the horse after a short conversation and start following him. Soon you will reach a small meadow. The painter will notice that his paints have disappeared.
Find the painter's paints
Activate Witcher Senses and look around. Find the paints and the footprints. Follow the smell that will lead Geralt to the entrance to small cave. Go inside into the deepest chamber where you will find a group of nekkers. Deal with the monsters. Don't underestimate them, they will be on 43 experience level - perform quick attacks, help yourself with ogre oil and North Wind bombs.
Give the painter the paints
After securing the cave find painting accessories. Take it and go back to the painter in order to give it back to him.
Now you can jump on the horse and follow the painter. You will reach a viewpoint which will be selected as the location of creating the portrait. After a short conversation Geralt will be able to select a pose for the portrait - the choice isn't final and you can check each pose before making the final decision.
Kill the griffin
The process of creating the portrait will be interrupted by level 45 griffin. Before starting the duel with the flying beast, put hybrid oil on Geralt's sword. Once the fights start, act similarly as when fighting griffin at the beginning of the basic game. Use crossbow or Aard sign to take the griffin to the ground. Once the beast falls down, attack it a few times before it regains strength. Don't worry about the painter - the beast won't be interested in him.
Go see your painting at the market
Once the griffin is defeated, a new conversation with painter will start. You can decide if only Geralt should be on the portrait or should the flying beast be there as well. Once the works are done, you will receive 300 crowns. Now you can wait one full day for the painting to be presented on the market in Beauclair. Go there to see the final effect and give your opinion about it. If you want, you can buy Portrait of Geralt for 1000 crowns and then hang it on the wall in Corvo Bianco.