The final Captain Toad level is definitely the most challenging, as you have to deal with a rising and subsiding lava. Note that you will need the use of the cursor/touchscreen for this level, so get ready to use it, especially in one instance where you have to act fast. Right at the start, drop down to the platform below you, then get on the other platform that’s right next to it. It should be pointed out that there is a Fire Piranha Plant in the middle of the level that will be shooting fireballs at you throughout your little journey, so keep moving to avoid them.
After getting on the second platform, wait for it to rise up, then collect Green Star #1 around the corner. Get back on the first platform and when the lava is low enough, drop down and quickly get on the next moving platform. When you can drop down in the next area, do so and wait on the safe platform for the lava to go down again. Once it does, quickly grab Green Star #2 from the little alcove, then return to the safe spot. Next, drop down to the pink pillar that you can extend with the cursor/touchscreen and get on the next safe platform. You now have to wait for the lava to subside one more time, but read what you need to do here, as you have to act quick.
Drop down and run over to the pink platform, then quickly raise it with the cursor/touchscreen before the lava gets you. Doing this will get you Green Star #3. As the lava is subsiding, drop down to the next platform, then once more to the pink platform that you will want to push up as soon as possible. Run along the donut blocks here and collect Green Star #4, then quickly move to the stable portion in the middle. Dodge the Fire Piranha Plant until you can drop onto the pink platform closest to the middle. This one will push you up to the clouds above the Piranha Plant, where you can collect some coins and the Stamp. Drop down the hole, defeating the Fire Piranha Plant, then collect Green Star #5 to finish the level.