You get the ability to jump on the Second exploration day! I'm not exactly sure what triggers Oatchi's automatic growth between exploration days, but all I know is if you get all the rescues and treasures you possibly can on the first exploration day, Oatchi will have his growth spurt allowing you to ride him and jump on the second (and final) exploration day.
Also, after your first exploration day, make sure to invest every single Pup Drive point into the path that increases Oatchi's Pikmin value so he gets at the very least the strength of 10 Pikmin so you can carry the blue onion back to the base while 30 of your ice Pikmin remain in the water. This was the trickiest part to figure out.
Another hint for practicing: what I do is I create a save at the start of Day 2 (the first exploration day) and copy the save so I can restart without doing the whole intro again.
TLDR it's totally possible to 100% the game in Day 3, after only two exploration days. I've yet to do it, but I've come very close two times...