GPW2 boss logic

Chuck:
Attacks alternate bouncing and footballs/rocks/baseballs, with which one from the latter set being randomly selected (although it will not do rocks/footballs if there are too many sprites onscreen). After five hits, the next bounce attack the boss does will have it split into three (unless there are not enough sprites to do so). The boss will attempt to whistle on the sixth hit.

Notably, the split attack can be skipped by doing 4 hits on the boss first, then waiting until he starts up a new bounce attack before doing any more. If you can get 6 hits from that point until he does another bounce attack, you'll kill him without him splitting at all.

The whistle attack can also be skipped if you get a hit on him immediately after he recovers from the sixth hit (effectively skipping that time), but I would not call that reliable.

When the boss goes into kamikaze mode after ten hits, he can not turn around while in midair. It may be useful to keep that in mind when trying to get away from him.


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Bowser:
As people probably figured out, phase 1 is three hits, phase 2 is two hits, and phase 3 is three more hits.

At the start of each phase, all of Bowser's available attacks (4 in phase 1, 9 in phase 2/3) are randomly shuffled into a list. Bowser will then cycle through this list, repeating from the start once the end is reached. As such, you can make some predictions about Bowser's upcoming attacks; if he does a shell attack at the start of the phase, you can assume he won't do that attack again until you see all his other attacks. However, the list is reshuffled each phase, so you can't tell anything about phase 3 from the previous phases.

The only exception to this rule is the 5-pillar attack, which is guaranteed to show up on every fifth attack. It is not part of the randomized list.

As for Bowser's hopping from side to side, it is a coinflip for which side he goes to, so you should generally assume he'll always jump. However, he will never stay on one side of the battle for more than two attacks in a row; he'll always jump on the third.