Water Change

I was just wondering if doing a 25% water change weekly would be enough to keep everything healthy, I was doing research online and everyone seems to say something different, I read somewhere that they do 100% weekly but wouldn't that put too much stress on the Axie?

What you really need is cycled tank/filter first that will keep the ammonia and nitrites down to zero and then with water changes you will take care of the nitrates.

Read on nitrogen cycle / beneficial bacteria , something to get you started : https://www.youtube.com/watch?v=PWoiCqCvJco

As long as you have established filter and you can match your tank PH/Temperature with your tap water and use some conditioner like API Prime, doing up to ~70% water change would not be an issue at all. 100% water change is over kill and I would not recommend it, it is doable if you can match everything but really unless you are sure of what you are doing i would do less, unless there is some severe issue with your water specs in the tank.

As for how often? then again depends is your filter able to keep up with the waste in the water , but doing more water changes cant hurt.

I base my water changes on test results, kinda like above said. Once you cycle the tank, you can base water changes on nitrates. Best to keep as low as possible unless you have plants (I don't encourage plants with axolotls ever though)