Hornet Man has a very garden-like stage, with some new threats you might not be ready for.
Throughout the level there are several "wrapping and unwrapping" platforms. To open them, shoot them, but be warned! They won't stay open long, and if you stand on them too long, you'll be flung to your death.
Another threat are flying scissor halves. The Jewel Satellite can protect you from these guys if you ram their first "half" unassembled bodies. If they unite, they'll boomerang back and hit you, so best to finish them while they're in a non-threatening phase.
You'll eventually come to a corridor where there are big ball-firing cannons. The cannon shots are needed to break the brick floors below and advance through the stage. You need to hit the cannons with a shot to make their shoot their ground-breaking shots. Be careful when doing this, you don't want to be fired upon by the cannons.
The halfway point comes in the form of a frustrating miniboss fight. Eight platforms in a room, with a "clock hand" type flower bar trying to knock you off. And a flower pot will randomly appear on one ledge, firing dangerous leaves at you. You need to shoot the flower robot while dodging the clock hand. For easiest results, use Tornado Blow. You only get four shots with Tornado Blow, but that's all it takes to kill this miniboss!
The rest of the level is more of the same, with the greatest challenge coming from "wrapper" platforms suspended over a bed of spikes, and more of the scissor guys trying to cut you down. Use Rush Jet if you need to.
Hornet Man waits at the end, and this guy isn't too hard. All he does is releases three seeker hornets, runs to the other end of the arena, and then does the same thing. Use Magma Shot. One well-placed shot can trash all three hornets before they can ambush you, plus he himself is weak to this weapon. Repeat this pattern and he'll die fast.
Victory gets you the Hornet Chaser, a useful weapon that sends hornets seeking after foes.