Turtles produce a lot of waste. There are different ways to deal with this:
1) massive biofiltration. Low maintenance, can be expensive. You could do this with canister filters, a big sump, plants, algal scrubber, etc.
2) large, frequent water changes. Relatively inexpensive, labor-intensive.
3) good mechanical filtration, cleaned frequently. Moderate in expense and maintenance time. The idea is to remove the waste before it decomposes into ammonia. HOB filters are good for this; powerheads help too.
Ideally you would have some combination of these three, with the difference being which you put the most emphasis on. I prefer to rely on mechanical filtration to remove most of the waste, so I can spend less money on biofiltration and less time on water changes.
Also, plants are great! Plants with roots in the water can consume huge amounts of ammonia. Peace lilies, dracaenas (including "lucky bamboo" and "corn plant", philodendron, pothos, sword plants, etc. are great for this task. Unfortunately, sliders like to eat plants, and all of these plants are mildly toxic, so only use them if you can separate your turtle from the plants. Floating plants such as frogbit, water lettuce, duckweed, and water hyacinth are also good ammonia sponges and don't seem to trouble turtles, though the last two at least are also mildly toxic.