The spitting brown monster has a projectile attack. This is the first monster you encounter that takes more than one hit to kill. Take them out as soon as possible. To effectively kill this monster without taking damage, wait for it to shoot, then rapidly tap while above it to take it out or at least deal a lot of damage before it shoots you again.
Upgrading the Sword stat in the armory strengthens your attack, reducing the amount of tapping you have to do to kill monsters, which helps when attacking monsters with projectiles, such as the spitter.