-To defeat the Puffstool in the Forest Navel with ease, beat him by yourself by punching him with Olimar. He does not do any damage but does take some time to defeat him. This will avoid losing a lot of Pikmin and health since the Pikmin attack you.
-Although it is true that Puffstool's spores do not damage you, it’s pretty inefficient to damage him with Olimar. An army of red Pikmin is the best way, but you have to do two things. First, while Puff is standing, have them attack its feet to make it fall over on its head and wiggle around helplessly. Some Pikmin will hang on to his feet while the others will fall off. Throw your red Pikmin on top. His underside is easily damaged, more than his head. However, it is unlikely you will kill him before he flips over and tries to spray your Pikmin, which turns them into Toadmin that will attack you. Press B to recall them before he flips over, which is about fifteen seconds. Bring everyone safely away from PuffStool and wait for it to spray. After the spores are gone, attack his feet and repeat the process. It should only take two times to kill him and get your part. Take the mushroom cap to make more Pikmin.