Outdoor axys, water filter?

I have some half grown axys out in a "pond", its aprox 400 L (100 us gal), free standing concrete, and they have a large clump of growning pond weed in there (which I transferred over from the fish pond of same set up). I left the bottom of the 'pond' bare, just added a few broken pots as hidey holes.
they seem to be doing well in there and are all happy, the ones that had the odd missing foot are all just about grown back. They water ok to look through for the first we while, but now It is rather green/filled with floaties esp near the bottom. A couple times I have siphoned the bottom and topped up with fresh water (or the rain has done it for me lol!)
But it is still murkey. I was hoping to help it remain clearer. What can I do?
One idea I though of was a solar pump, that would run into a filtering system- something like sand/gravel/filter wool?? either in a container/bag within the pond so that it just takes out the debris and only clear water runs back in ?

any ideas?

I don't know if water hyacinth is legal where you live. Water hyacinth does clean the water, offer shade, and cool the water. It is a nuisance in nature but works great in controlled systems.

Just looked it up, not allowed here

I was thinking something like this?
Seeding DIY Pond Filter - YouTube

So I am looking at getting a pump, I really do not want to over do or under do size...
Is 200L per hour ok for 400L 'pond'? I read on line that it should do the contents of pond every 2-3 hours, I didn't want to over do it at all and cause too much water disturbance for the axolotls.

I was also looking at solar pumps, but would this effect the filter- ie the bacteria in it? and cause problems it only being on in daylight hours?
I was then thinking that it would need to work more during the day to make up for lack of filtering at night?

I think I have decided on a simple idea of a garden pot hanging on the side in the water ,full on sponge media and a pump pumping water from the bottom of the pond, up and into the top of pot, water runs through sponge, collecting all the floaties, the through holes in bottom of the pot back in the pond..

I use a solar powered aerator in some of my tubs, but this only works when the sun is out. I have since seen one that will charge a battery so when there is no sun it will still work for a period of time. I think you will need to have a filter running all the time to be effective.

I was thinking it might be a waste of time. the main pro to it would have been wiring, If I can find a cheepish pump with a long cord it would save a lot of hassel - no worrying about a join + water/rain!