Wave Man should be the first robot master to challenge, because special weapons are absolutely useless during his stage. In fact, in the first part there are no enemies that can be defeated, while in the last part Mega Man can only shoot from the cannon on the watercraft he's riding.
Wave Man's stage presents you with some interesting challenges, but it's nothing you can't handle.
Throughout the stage, you'll end up facing broken pipes that vent steam. Dodge this, it's as harmful as any enemy.
About halfway through the stage, you'll encounter a scenario of bubbles being propelled upward, big and small. The big ones don't pop, and you can safely stand on them, but the little ones will pop after about a second of you standing on them. To successfully reach the next area, you need to jump back and forth between the two big bubbles, using the small ones at platforms. It sounds tricky, and it is. Just stick it out, and it's not too tough.
For the final third of the stage, you're forced to pilot a jet ski-like contraption. Several aquatic enemies will try to deep six the Blue Bomber, so keep firing and avoiding shots. You'll encounter a mini-boss in this area who surfaces and sinks, and he fires at you when you surface. Dodge his shots, and shoot the green spot in his forehead.
The Beat Letter is after the mini-boss section. It's floating above you in plain sight, but you may have a hard time getting it due to all the action on the screen. Just concentrate and don't let it pass by.
Wave Man fights in a pretty predictable pattern, and he's not too tough to bring down. His weapons include water from the floor made to gush up at you, jumping, and fired harpoons. Dodge all of this stuff and bring him down with the Charge Kick, if you have it. The secret to winning this fight is to be on your toes and focus on dodging whatever he throws your way. Only attack when you know you can do it safely.