Since this is downright insane tatting (don't know whether I'm ever going to do another one), I will just give a rough description of what I did. Other than a good understanding of square rings you need to be well versed in using split rings, know pearl tatting, and working with beads.
I used two shuttles of Anchor crochet cotton no. 40 plus two shuttles of sewing thread (these made the draw threads for the square rings). The sewing thread was the same color as the crochet cotton. The beads (no. 14) were prestrung on both crochet cotton shuttles.
The straight parts of the necklace are done in pearl tatting using both sewing threads as core threads. It is just the basic pattern - 1 ds using each of the crochet cotton shuttles as ball threads alternately.
In the square split rings one sewing thread acts as draw thread for each half of the ring. You make 4 ds with both shuttles, 1 ds with 1 shuttle only, picot with 4 beads, 1 ds with 1 shuttle only, 4 ds with both shuttles for the first half of the ring. The same number of stitches - only 1 bead for the picot - was used for the second half of the ring.
I'd recommend working on a surface, so that the shuttles won't dangle that much (they will still do enough of that!). I also recommend not doing too long times off that project, since every time you do you will have to think through how it was worked and get back into a working rhythm. With medium tatting speed this should need about a week if worked on every day for one or two hours. Designed Summer 1998