There is no door 4; there is another balloon down in the water area.
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There is a hidden door by the things on pedestals. look around for i think a dive hole or hidden door that has lights coming out of it.
you open up the door in the hidden lake
If you mean the one by the underwater cave you have to follow the squid on the first level of rescue the black puffle there is a squid follow it and you will come to a door which the key is hidden in.
you have to do 350 battles. Finish the subspace emissary mode then go to the swamp level find a secret door in the area after giant diddy then defeat jigglypuff.
You will get the key when you have rescued the black puffle in puffle rescue three times it does not work