How can this be done?

I am making an AoS map based off the Squaresoft PSX RPG, Legend of Dragoon. I have the game, and was wondering:

Is it possible to extract voice clips from fights so I can import them into my map? Like say, in the game, whenever the main character, dart, uses a spell like, say, Final Burst, he will shout "Final Burst!" as he does the attack. So I was going to stick some of these into my map as triggered when the appropriate abilities are cast(not on all abilities, just some, otherwise people would be driven nuts by the soundclip spammage).

How would I do this? Can it be done? What type of extra software would I need, if any?

*PSX* RPG? So I would presume it's on a Playstation?

Well, if it's on the PC or an emulator, you can easily record any sounds out using Goldwave and this tutorial of mine:
http://savage.samods.com/tut02.htm
But unless you can turn off music and other effects, you may not be able to get it purely.

The alternative to that, then, is a third party (fan made) program that lets you directly view the archived data files (Presuming they are - most games are so, few have an open directory of all the files), like an MPQ Viewer for WarCraft 3. Try download sites for the game or ask on forums for it.