You can go to the large field on the northeast from White Orchard village. Meet Vesemir again and confirm that you want to place the bait. You will receive a crossbow that can be used for ranged attacks (it has unlimited number of bolts). After the battle with Royal Griffin starts, pick the crossbow from the menu and test it. During this battle use the crossbow always when the griffin flies above the battlefield. It will force him to land. Watch out for monster attacks done from air, jump away from them as soon as you see that the enemy is flying towards you. After the griffin lands, attack him with the silver sword. Using Aard sign to stun the flying beast is a good idea. It will allow you to perform strong attacks and you will have to dodge enemy attacks less frequently. During this battle, you should drink Thunderbolt from time to time, it will make your attacks stronger. Don't forget about observing your health bar.
Keep attacking the griffin until he loses about half of his health bar and leave the battlefield. Activate Witcher Senses, they will help you determine that the monster hid near the Mill, North from the battlefield. When you find him, resume the battle and keep using the previous tactics. After you kill the beas,t examine the griffin's corpse to gain Griffin mutagen and Griffin trophy. Place the mutagen in the correct inventory slot (it will increase Geralt health bar by 150 points - later in the game you will be able to experiment with it further). Now you can return to the garrison commander in Nilfgaardian camp and inform him that the beast is defeated. For the first time in the game, you will have to make a decision within the time limit. You can either take gold from Gwynleve (you will receive 150 crowns and 300 experience points) or refuse taking the reward (you will receive 500 experience points).