My favorite memory is the moment, when I saw whales jumping out from the water!

It was an amazing moment, because they are big animals.

Also, it was like an impossible mission, because our captain was following their signals to give us this amazing moment.

For both commas before "because", no comma is needed since the "because" directly explains why what happened before the comma occurred.

My favorite memory is the moment, when I saw whales jumping out from the water!

The placement of the comma is rather awkward and unnatural.

Also, it was like an impossible mission, because our captain was following their signals to give us this amazing moment.

(1) "An" is used before words that start with vowel consonants.
(2) It's not very clear who "their" in "their signals" is referring to. Perhaps it might have been good to clarify this explicitly in your writing.
(3) The repeated usage of "moment" might sound stiff. Alternatively: "...to give us this amazing view."