Notice that she often uses plurals where she should use singular words (maybe a plural form felt stronger in her opinion): cousins, aunts, Allisons, mums, sisters haircuts (according to her parents, she only had one of each).

SHARK= A big and powerful fish, sometimes man-eater (see picture)

WHOLE= Complete, entire.

I LIKE ANYTHING= very probably she means "I like everything". Anyway, ANYTHING can also mean "I don't care what, all things are fine".

HAIRCUTS= The style of your hair (wrong pluralisation again)

PYJAMAS= Night clothes consisting on lose trousers and shirt (see picture)

STUFF= (coll. esp. AmE) Things.

I CAN DO ANYTHING GOOD= I can do everything well (using an adjective instead of an adverb is frequente in colloquial English, especially AmE) (she's very probably using "anything" when she means "everything" once more)

---------- FAQ* for this video ----------
Q: How old was Jess at the time of the video?
A: She'd turned 4 about 6 weeks before the video was shot.

Q: How old is she now?
A: Depends on when you're reading this, but she was born in late October of 1997.

Q: What does she say at the beginning?
A: Though some claim they hear the word "assert" - as in assertive - she's actually saying I can be a "shark" - but it sounds like "sark" because she was incapable of making "sh" sounds at this time.

Q: Are you sure she's not saying "I can be a SARK?" Her daily affirmations are consistent with the teachings of the author SARK.
A: This is an interesting coincidence, but a coincidence nonetheless.

Q: Does she say, "I like my 'elephants'?"
A: More than one person has thought that, but she's actually saying I like my "Allisons." Allison is her aunt.

Q: Does Jess have more than one mom? She says I like my "moms."
A: No, she just has one mom and one dad (me.) For some reason she was "pluralizing" several things in her "like list." That's why she says "Allisons" and "cousins" (she only has one.)

Q: What does she say at the 22 second mark?
A: I really don't know, though I do have a theory now: this video was taken right around Christmas-time, and it ALMOST sounds like she's saying "I like my presents." So that's what I think it is - but I could be wrong.

Q: Did she do this affirmation every day?
A. Yes, until the age of seven. ... Just kidding. :-) I think this was a day when the video camera was out, so there was an element of "putting on a show" - but Jessica still meant every word. Though she may have been hamming it up a bit, she was sincere in the things she was saying.

*FAQ= Frequently Asked Questions.  Q= question / A= Answer (father's answering)