Hold down the crossbow button to aim, if you tap that button it shoots targets automatically.
Confronting that beast at a higher level won't make that fight easier enough to be a real difference maker, that griffin is within your level range from the very start after all. In all honesty your gear will make more of a difference there, but again it won't be huge.
What you really need here is some skill. Learn how to avoid the griffin attacks and you'll slice it up just fine. If it attacks with a leap from a distance, then roll away sideways, don't dodge it won't be much help. If it's about to hit you with its wing, you can dodge skillfully right under that wing and get an advantegeous position behind the griffin and land quite a few hits before it recovers. Timing is key for this and can be a bit tricky to get it right, but when you do at least once you'll pick up on that idea quite easily afterwards. Dodge a moment before it actually swings that wing, that griffin does that with a short delay, first it readies its strike.
And of course use other tools at your disposal. Make sure to craft a swallow potion before the fight, it heals you over time but does this quite quickly, especially if you stack it with some food. Tawny Owl potion (available from the very beginning) will increase your stamina regen and allow you to cast quen more often. Speaking of which, quen always absorbs most if not all damage and allows to correct for those mistakes or rather mitigate them. Same goes for the thunderbolt, make sure to craft it and use it in the fight, it adds to your damage, Vesemir gives you the recipe and ingredients needed to craft it when you go hunting with him. Last but not the least, igni can set that griffin aflame dealing a lot of damage to it, the exact chance of that can be viewed in character stats, it won't proc that often at that stage of the game though, but there are ways to increase those percentages to a reasonable number before the fight.