Brilliant!
What size mixer?
What size barrel?
What size inner mesh?
I am rather proud of coming up with the idea to use eye bolts on the mixer barrel instead of drilling holes into the side of the mixer barrel to mount D rings. The eye bolts accomplish the same thing - which is to attach a sifting barrel to the cement mixer. With the eye bolts, I can remove them anytime and restore the cement mixer to the original condition if needed.
My cement mixer capacity is 4 cubic feet, which I believe is the standard size home cement mixer. You can buy smaller cement mixers for home use and I expect they would do just as well for sifting compost. I would have been happy with any old used cement mixer but could not find one for sale where I live. So, I had to buy a new mixer.
My shifting barrel was a 55 gallon food grade plastic barrel. I had previously cut the barrel in half to make 2 planting barrels for the yard. However, Dear Wife preferred wooden half barrels so I had the plastic barrel halves sitting behind the garage. I took one of those half plastic barrels and cut it in half again, using the bottom of the plastic barrel, then I attached about 2 feet of 1 X 1/2 inch wire, then the top strip of the plastic barrel. I overlapped the wire in the plastic barrel about 3 inches for support. So, the amount of exposed wire for sifting is about 18 inches long. FYI, the barrel is about 2 feet in diameter which makes about 6 feet round circumference for the wire sifting. That is why the sifting goes so fast.
I wanted to sift my compost finer than a 1 X 1/2 inch mesh, so I have made both a 1/2 inch mesh insert and a 1/4 inch mesh insert. I have been using the 1/4 inch mesh insert and the compost is extremely fine and light after sifting. You could use it for potting plants. The inserts can easily be swapped out for a different sized wire mesh. I use cheap plastic zip ties on the wire mesh to hold it in place, so it takes very little time to cut the plastic ties and swap out an insert.

I used to spend hours every year manually sifting compost on my good old 2X4 wooden frame compost sieve to get very little compost. Now, I can sift a garden cart full of compost in about 20 minutes - which would have taken about 3 hours to do by hand. We pay about $5.00 per bag of compost where I live, so within the first few uses of this cement mixer/compost sifter, I figure this project has already paid for itself.
Plus, my wood chip compost or the chicken run compost is just so much better than the big store compost. The big store compost bags would have to be sifted anyway to remove the "garbage" that always seemed to be hidden in the bagged compost (plastics, rocks, metal scraps, etc...). So I am very happy with my investment in the cement mixer/compost sifter project.