Why did Moshe need to cry out to Hashem? Why did Tefilah alone not suffice?
Seforno: Because some of the frogs (crocodiles) would remain in the Nile, and Hashem does not generally work in halves. 1
Sifsei Chachamim (6): One should pray audibly to his own ears (Shulchan Aruch OC 101:2). Due to the terrible racket caused by the croaking of millions of frogs, he needed to scream to hear himself.
Moshav Zekenim #1: He wanted the magicians to hear him above the frogs' croaking [lest they think that he removed them through magic, and not through Tefilah].
Moshav Zekenim #2, Rosh (14): Moshe attributed greatness to himself (Hispa'er Alai). 2
Sanhedrin, 64a (Seforno).
Abarvenel, Ibn Ezra: Moshe did not ask Hashem if He will send them whenever Pharaoh wants. Perhaps Hashem wants the Makah to last a week! (Perhaps this is the intent of Moshav Zekenim and Rosh. Alternatively, Moshe was worried lest he be punished for aggrandizing himself, and Hashem would not fulfill his prayer.