Not everything in the forest should be fought. This is how to deal with the main threats.
Never fight: the Deer and the Ram
Both are immortal. The Deer hunts in the dark and is pushed back by light. The Ram arrived with the Volcano update. Learn where they go and stay out of their way.
Fight carefully: wolves and bears
Wolves guard the first locked cave and the Dino Kid. Alpha Wolves and bears guard later caves and camps. The Polar Bear has around 500 health and hits for about 50, so bring food and armour.
Expect them at night: Cultists
Cultists serve the Deer. Regular Cultists come with Crossbow Cultists, which shoot from range, and Juggernaut Cultists, which have armour and swing morningstars. Defences around your camp handle the raids better than fighting in the open.
Late game: the Cultist King
The Cultist King is a summoned boss in the Volcanic biome. Go in with your best gear and a full team. The rewards include Wildfire and Infernal weapons.