Ring Half 2

Technically the Second Hippo is the screen before the checkpoint. See notes on Hippo one, and pass this screen in roughly the same fashion.

There are two long screens (with a short screen thrown in) to end the stage.

Main Strat - Use Pharaoh

Checkpoint Screen

The checkpoint screen has a slowly rising stair case full of spinny enemies, followed by another disappearing bridge section. (It starts with the ladder overhead that leads to an Eddy screen.)

Start holding a Pharoah charge. Jump over enemies 1 and 3, use charge Pharaoh shots on the second and fourth enemies.

On the bridge section, your goal is to destroy enemies while sliding as much as possible, both to move fast and to not fall through the platforms. Keep in mind that sliding from the start of the platform (the big block not the bridge) will keep Mega Man's hit box off the ground, delaying the bridge's disappearing pattern.

Jump to the first bridge, shoot and slide. 

You can shoot a normal Pharaoh shot from under an enemy, and the shot will destroy an enemy over your head.

You can make the jump under the last Saturn enemy on this screen if you're fast. If you kill the enemy (possibly with an up-angled Pharaoh shot), remember to HOLD A through the jump in case you collect a drop.

Backup - Use Bright

As for most of the second half of the robots, Bright Man's Flash Stopper is the ultimate backup. Remember the Saturn enemies will not move and you will not have charge shots or angled Pharaoh shots, so adjust your shots (or wait for enemies to fly into range) as needed.

Final Whopper

Optimal speed is to slide through the whopper, just remember it does 8 contact damage.

If you are low on health but have over 4 HP, stand on the ledge of its platform and look left to back boost through. The ring shot will deal 4 damage and give you a chance to slip through. (You could also opt to do this simply to save 4 HP over contact damage)

Whichever option you choose, move quickly. You are likely down to your last hit, and you do not want to find out how long it takes Whopper to fire a second shot.

(You may, of course, also defeat the Whopper as intended. Watch your Pharaoh Ammo if you do, and be careful dodging the rings.)