Before you actually start doing the boss rush. A mini boss appears at the beginning. Thankfully, it won't take long to get pass. You are in a huge room filled with eight teleporters. Each leading to a different Robot Master. You do have enough time to decide which side of the room you want to do first.
On the left side you have Tengu Man, Clown Man, Frost Man and Grenade Man.
Tengu Man
Ice Wave
Clown Man
Tornado Man
Frost Man
Flash Bombs
Grenade Man
Thunder Claw
On the right you have Astro Man, Sword Man, Aqua Man and Search Man.
Astro Man
Flash Bombs & Homing Sniper
Sword Man
Water Balloon (top half only)
Aqua Man
Astro Crush
Search Man
Flame Sword
Alright I will give you some tips on a few of these Robot Masters to help you out. Tengu Man can be frozen while on the ground allowing you to give him another direct hit. Thunder Claw can send Grenade Man's grenades right back at him. Astro Man can be harmed by both Flash Bombs & Homing Sniper.
Homing Sniper ends up being easier since it does follow him. Actually if he's a little not far from the ground. You can repeatedly jump then fire Homing Sniper a couple times to speed up the boss fight. Keep in mind, sometimes Homing Sniper targets the orbs instead of Astro Man.
Astro Crush is only four uses but does a lot of damage to Aqua Man. Sadly, only your Mega Buster can work on him. I highly recommend learning his patterns then keep firing at him rapidly when in close range. Search Man likes to hide in one of three bushes, Flame Sword can quickly burn them away.
But if you end up hitting him while behind a bush will instantly take the other bushes away. His projectiles can be a little tricky to avoid. Other than that, most their weaknesses will greatly take their health down. Some more than others like Clown Man.