This is not necessarily a hard combination to do but it take a little "elegance" to pull off :)
Make sure you know how to do a basic Egyptian shimmy first and the chest circles and half circles, then attempt to put the 2 together and that's the challenging part. This combo goes well with a steady shimmy beat that is usually a 2 count and ends with a strong beat at the end of the 2. So you would shimmy while doing the half chest circle for 2 counts and end it with a chest drop to mark the strong beat. Of course you can skip the chest drop part if your beat is a steady shimmy beat.