False Knight (required)
Hornet (optional)
Hornet isn’t entirely a required boss to beat Hollow Knight, but if you don’t beat Hornet then you don’t get Mothwing Cloak (Dash) which will make much of the rest of the game harder to beat.
Hornet has four attacks. First, she throws her nail at you. During this attack you can get a few hits in if you’re quick, but remember to jump again as the nail comes back towards Hornet. Second, she dashes at you. I usually jump this attack and then get a quick nail hit on her as she passes beneath me. Third, she jumps into the air and dashes downwards at you. I often jump this and down strike with my nail to get a hit in. Finally, she uses the silk in her nail to create an area of affect damage. I simply avoid this attack, though you can hit her with a spell if you have the Soul for it.
Mantis Lords (optional)
The Mantis Lords are optional but they do reveal a path to different areas of the game that have many excellent charms and spell upgrades. If you have Mantis Claw you can jump up the far left wall of the arena. At the top of the arena is a Lifeblood Cocoon you can use to get some extra health before you fight the Mantis Lords. Check out the first video for the location of the Lifeblood Cocoon.