Is there a way I can use Action Replay Powersaves on Ubuntu/Linux?

I guess you won't get far with it.

You may want to use wine, which will emulate a Microsoft operating system and start the Action Replay software in it.

You will have to look up for a tutorial how to create an environment for your desired deeds. But wine is really easy to go with.

Though I have one of these Action Replays myself here, I unfortunatelly don't have enough time to test it myself. Never used it though. Why have I even bought it?