Hi jawiest, the main problem with your model is that at every place you have curves meeting up they are not tangent smooth to each other, they have a slight crease:





This kind of thing where curves are not smooth to each other but only a little ways off makes things difficult for filleting. So the main thing to do for your case here is to improve the quality of the curves before you extrude them. The curves need to have their first 2 points in line with the first 2 points of the next segment so they are tangent to each other instead of slightly creased at each place that 2 segments are touching.

- Michael