Once you reach level 2+ and own a couple of Thunderbolt Potions to increase your power for 30 seconds, you can go for your first boss: the Royal Griffin. The Royal Griffin has two main attacks in its first phase that you'll need to watch out for. When you first encounter it, it'll most likely circle around you in the air, getting ready for a dangerous dive attack. Prepare to roll out of the way.
If your aim is good enough, you can also shoot it out of the sky with the crossbow Vesemir gives you. This causes the Griffin to fall onto the ground, allowing you to get a few extra hits in. If you're quick enough, shooting a crossbow bolt at the Griffin right when it tries to take off again will keep the monster grounded, allowing you to resume your sword attacks.
If you choose not to use the crossbow, there's one more ground attack that you'll have to watch out for. When on the ground, the Griffin will attempt to swipe at you with its claws.
Once you've gotten the Griffin down to about a third of its health, the monster will fly off once more. This time, it's flying to escape. Call for your horse and quickly pursue the Griffin. Don't worry if you lose sight of it; Geralt can use his witcher sense to track the beast down. When you've caught up to it, this will mark the start of the final phase of the boss fight.
During this phase, the Griffin emits a sonic wave that will damage anyone standing in front and to the side of it. This attack has a fairly wide range, so you'll want to stay behind the monster at all times. Apart from that, the Griffin's attack patterns remain the same. Another thing to keep in mind is to make sure Geralt uses his silver sword for this fight.