• You play in normal mode.
  
  
  
• You already have Twin Pistols 10^16 or Level 2 Cannon

Part one is the easiest part.
I bet you can beat this part without taking any damage without even taking any guide.
But if you need some advices, I can only say just do hit and run, beware of bugs launched by bug cannons.

This is the hardest part, but still easy in general.

Before the enemy launches attacks, go and run to its back, and attack it with cannons repeatedly while still being careful as there are some of its attacks that can go backwards.

Last part before you get both of Queen Bug Regicide and Queen Bug Master, if you do well.
Take a safe distance, I recommend attacking from here (see picture) because based on my experience there aren't many enemy attacks going this spot.

Tbh Queen Bug's the weakest enemy in-game (story based, it's the strongest), because it can't move anywhere so it's easier to find its attack patterns.

Congratulation! You got both of (if it's your first time defeating Queen Bug)
Queen Bug Regicide
Defeated the Queen Bug.



and
Queen Bug Master
Defeated the Queen Bug without taking any damage.