This looks more complicated than it is. There are no joining picots to worry about as the 2nd colour is used instead.
Here is the pattern. M is the main colour, C is the contrasting colour.
Rings 1-5: 4 ds in M, p, (ds in C, ds in M) 4 times, ds in C, 4 ds in M, close ring, fasten off, tie ends together and sew them in.
1. Start off as normal with a slip stitch and work 4 ds.
2. Using the contrasting colour, make a ds on the hook. You do not need to start with a slip stitch. The end will be sorted out later.
3. Using the Main colour, make another ds on the hook. Take care to carry the main colour at the front of the work and the contrasting colour at the back of the work.
4. Carry on adding the ds as in the pattern. Your work should then look like this.
Close the ring as normal. Your ring should look like this.
5. Work the 1st 4 ds of your 2nd ring in the main colour as normal. When you work the next ds in the contrasting colour, work it as close to the 1st ring as possible, without pulling it too tight.
6. Complete the ring.
As you can see from this picture, the contrasting thread connects the two rings acting as a joining picot would.
Complete the rest of the rings and fasten off.
Tie and sew in the ends as normal, making sure that you complete the connection for the contrasting colour between rings 1 and 5.