Over the past few years, there have been many queries to me about this, so here is a status report.
The full pattern was published in Moje Robótki 8/2007 (a Polish needlecraft magazine). After several re-issues, it doesn't seem to be available from the publisher in Poland any more, nor are many owners of the pattern willing to sell it on. The pattern was not included in Jan Stawasz's two books. Surely it will be included in his third book of patterns – but we are all still waiting… (If you have managed to obtain a copy of this pattern, you should check out the lists of errata available in Facebook and Craftree – more details below.)
Anyway, for those determined to tat this doily and still seeking the pattern, there is now an alternate route! It's called the "Frankenstein Monster Doily" – Frankenstein, because the rounds were cobbled together from other doilies published in Jan Stawasz's first book, Tatting Patterns and Theory. So now, to tat the Monster Doily itself, all you need is a copy of this book, and the "recipe" for it.
That recipe was worked out and tatted by Marla Nikirk – many thanks, Marla! :-)
It's available in the Facebook Group "Monster Doily by Jan Stawasz", under the Files tab. Another place where you can find it is as an attachment to the database record for the doily in Craftree (https://craftree.com/patterns/1006). (You need a free membership to access this page.)
At this time, Jan Stawasz's book is available at tatting online shops such as Handy Hands (https://hhtatting.com/product/tatting-theory-and-patterns-jan-stawasz/) and Tatting Corner (https://tattingcorner.com/index.php?main_page=product_info&cPath=1&products_id=350). I recommend that you get both his books before they run out of print again.