Here are some suggestions for you:
1. I saw a movie about a giant gorilla.
No change needed to this sentence.
2. A young woman was the gorillaís friend.
This is okay but I'd probably say something like "A young woman had a gorilla as a friend." There are many options here though, and yours is not incorrect...just sounds slightly unnatural to me.
3. Because the animals couldnít board an airplane, she took the gorilla by the airplane to America furtively.
Some changes are needed here. I think you mean "as a fugitive" or something similar, but that probably won't work. It's hard to say without more context, but perhaps one of these options would work here:
"Because wild animals are not allowed on airplanes, the woman took the gorilla to America on a boat."
"Because wild animals are not allowed on airplanes, the woman snuck the gorilla into the baggage compartment."
4. The gorilla was found and sent to a special zoo.
5. He didnít like the zoo.
6. At that time, there were some hunters trying to kill him.
Also okay, although a slightly more direct structure would be "At that time, some hunters were trying to kill him."
7. Then, he escaped from the zoo and ran away continuously.
"Ran away" is at least partially redundant with "escaped." Also, the way the sentence is written, "continuously" does not fit with "ran away," which is written as a verb with a definitive endpoint. One solution might be "Then, he escaped from the zoo and stayed on the run for a long time." Of course there are many other options. You could also probably drop the word Then.
8. Finally, the woman found him and stopped the killing and saved the gorilla.
This is a list and, in my opinion, would read better if it were punctuated. APA, Chicago, MLA, and other major editorial styles in the US would all require the final comma in the series: "Finally, the woman found him, stopped the killers, and saved the gorilla." (Note the change from "killing" to "killers," which makes more sense given the context of your story).
Hope that helps! Good luck! :)