Plant Man is another Robot Master with a pretty straightforward stage, there are just a few things you need to be aware of before attempting it.
Twice in the stage you'll encounter a bulldozer mini-boss. This guy is vulnerable in the head, so shoot him there. If he gets too close to you, and you fear for your life, shoot him in the lower "hand" area. Your shots will bounce harmlessly off of him, but you'll push him back and keep yourself safe.
Near the end of the stage, you'll have to traverse a spring-filled marshland with plenty of instant death situations. Dodge the robots that try to push you to your fate, returning fire when you can. While on the springs, holding the jump button will allow you to jump super high. Those flashing flower cores at the top of the screen are actually energy pellets, so jump up and grab some!
Plant Man is a joke of a boss. He's a carbon copy of Star Man from Mega Man 5, and he's even easier. He'll put on his shield, do a jump, and throw the shield at you, repeating this for the entire battle. He's only vulnerable when he's without the shield, so when he throws it, kill him with extreme cold from the Blizzard Attack.
Victory gets you the Rush Jet.