03. Mushroom Way
First Screen
Avoid the enemies and make your way to the exit, ignoring the trapped Toad along the way.
Watch out for the Goomba that appears out of the exit! He appears right as you get there if you're really fast. If you're a little slower, he should be already wandering around by the exit, so just jump over him.
Second Screen
Grab the flower from the chest on the left island without a fight by following the instructions below.
Position yourself alongside the flower directly to the left of it, pressing up against the flower. You should not contact the Goomba as long as you're on the ground.
Jump and move slightly to the right so you land on the very left edge of the flower. You should now be standing on the flower next to the Goomba without triggering the fight.
Jump directly to the left while holding the run button to make it to the island.
Third Screen
Take the top route and watch out for the Spiney that comes running out of the bushes across your path. Jump over it and keep going to the Hammer Bros. fight.
Hammer Bros.
Use Jump on one Bro, then block both their attacks.
Use Jump on the other Bro, the block two more attacks.
Use an untimed attack on a Bro you dealt more than 40 damage to with Jump (should be either of them if you properly timed your previous jumps). This one should fall.
*Remaining Bro uses Vigor Up*
Use an untimed Jump on the remaining Bro to win.
Bad RNG here would be multiple uses of Hammertime. It wastes time, but you can block it.
If you dealt less than 40 damage to the Bros (or you just want to be safe), use a properly timed attack/Jump for the last two turns (slightly slower).