Aki is a very odd collection of First Nation reserves, national parks, forests and plenty of other areas in-between. I had a look at the massive map provided by UNESCO and there are plenty of sections I don't see as nature protected yet I guess they are part of this cultural aspect. More on that later.
There are a few feasible ways into this grand area, a massive collection of several parks. I have been to two of these. Unlike Nahanni it doesn't require a splurge but instead some determination, time, and gravel roads, lots of gravel roads. First stop was Red Bay in Ontario. From there we canoed along flat lakes and marshes towards Douglas Lake. It takes a long day of paddling, camping at the shore, and another full day paddling back. As the drive from Winnipeg is 5h each way it took 4 days total. At the park we mainly saw ducks and other birds but no mammals. The Woodland Caribou park is unfortunately only home to a few thousand of these. The issue is that they eat lichen and logging around the areas has killed those. Second is that their migration paths are now destroyed due to human influence and being stuck in such a "small" area is unnatural for them. Hard to believe with the vast provinces but it is unfortunately true.
Friends of mine went canoeing all the way from here to Bloodvein in the west. Crazy if you ask me even for Canadian standards but I also don't have 3 weeks to spare. Instead we drove through the buffer zone Nopiming Provincial Park for some hiking, then camped at Wallace Lake (still in a buffer zone, South Atikaki) to take a boat out onto the lake. It doesn't cross into the core zone and isn't spectacular in any way. I don't recommend this as it is expensive to lodge here. As a lodger you are allowed to use the ramp so theoretically you could bring a canoe or boat and paddle into the core zone from the south.
The next day we drove up to Bloodvein itself. There is a new gravel road and a bridge across the Bloodvein river to enable this journey, although before there was a ferry service from town instead. This section is surprisingly included in the inscribed area. So far we hadn't anything for the cultural part but even at the reserve it was not clear, I believe this is another one of those "landscape" situation where history and long term cultural behavior is just something we need to assume to be there, although if you go further into the park there are pictographs to show the long relationship between First Nations and the park. As you can tell I'm not a fan of this part too much.
Overall visiting areas at the edges of the park weren't all that exciting, and there isn't much unique here compared to other parts of Canada. I am happy nature is protected and gets recognition but that's about it.