You can face the first Forest Ancient in God of War Ragnarok during the main quest The Reckoning in Vanaheim. From the walkthrough, you will learn what the Forest Ancient's weaknesses are, as well as how to avoid the boss's ranged attacks.
Location of fighting the Forest Ancient
Forest Ancient is one of the game's mini-bosses. The first mandatory battle with the Forest Ancient will happen during the main quest The Reckoning in Vanaheim.
You will encounter the Forest Ancient shortly after leaving Freyr's camp. The fight will begin after approaching the Forest Ancient (you can attack him with a surprise ranged attack).
Later in the game you will be able to encounter more Ancients. The main tactics are always similar, but they can differ between "variants".
Tactics for the encounter
The Forest Ancient's main attack is to open the chest and shoot - the enemy can bombard the area or shoot horizontal beams.
If you don't have time to attack, at least try to stand behind a tree so that Kratos doesn't get hit with the beam.
Try to quickly throw Leviathan at the opening in the chest. If done correctly, the Forest Ancient will drop orbs.
You have to pick them up and throw at the boss. Each throw will deal massive damage to the Forest Ancient.
There is a good chance that the orbs will also quickly charge the white bar and stun the Forest Ancient. Run up to him and press R3 to use a strong attack. You probably won't kill the boss this way, but you will take away a good chunk of his health bar.
In the later part of the battle, the boss's minions will appear. Do not ignore them, as they can be a big problem when fighting the Forest Ancient. Try to eliminate them from a distance. If a monster jumps on you, quickly press X to drop it.
Continue attacking the boss. Once the Forest Ancient loses his entire energy bar, he will fall to the ground and explode.