As Wood Man launches his leaves, watch until he throws his Leaf Shield, jump over it then continuously shoot him with the Mega Buster. Be careful of the falling leaves above you. Prepare to jump over the swaying leaves as they fall. As he's nears you, run under him after he throws his shield. Run to end of the room opposite him then attack him again. His attacks deal a lot of damage to you so you need to beat him swiftly.
Wood Man is weak against a lot of weapons. The most effective among those is the Atomic Fire, which you can get from Heat Man if you defeat him beforehand. Charge the Atomic Fire to its maximum & release it after Wood Man throws his shield. You can defeat him with two fully charged Atomic Fire. Another weapon is the Metal Blade, just do the strategy above. Another is the Crash Bomber, but you have to use it while Wood Man has his shield on. The explosion will deal damage to him multiple times. In Easy Mode, the Air Shooter can give him great damage & can go through the shield if you are close enough.
In Dr. Wily Stage 4, you will encounter Wood Man again for a rematch. The Atomic Fire is the best weapon to use against him as the other weapons mention should be saved for Wily Machine No. 2.