Which parts of Candide would be most disturbing to a European monarch?

I think the easiest and most obvious answer to this question would be to point towards chapter 26 of Candide, in which Voltaire turns his vision of arbitrary fortune to reflect on the monarchs themselves. In this chapter, rulers are shown to be just as subject to these cruel turns of fortune as every other human in the book. Cruelty abounds everywhere, and no one (not even rulers) can ever be secure against those tragic twists of fate.
Taken from a personal perspective, one can imagine the thought of being deposed or overthrown would be greatly disturbing to any given monarch. That being said, I suspect in most cases, any particular scene within Candide taken in isolation (even a scene such as that depicted in chapter 26) would be less disturbing than the effect of this book when it is viewed in its entirety.
The thing you must be aware of is that monarchy lay at the very center of the early modern state. Thus, monarchy was actually very closely intertwined with all the various other institutions of the State, including the army, the church, the nobility, and the judiciary. It stretches over any number of relationships with various cities and provinces, as well as with all the various sub-classes that made up the early modern social hierarchy. One might say that the monarchy was the glue that held this entire political system together. Meanwhile, taken as a whole, Candide represented an attack on that system.
With that in mind, I think it would be somewhat deceptive to single out any chapter in particular the way one can single out attacks on the Church or the nobility (to give two examples). On the contrary, any attack on traditional religion is also, in its own way, an attack on the monarchy. This is because monarchy ultimately gets much of its legitimacy from religion and is closely tied up with traditional religion and religious structures (think about something like the Divine Right of Kings). Something similar might be suggested of any attack on Nobility: to undermine the nobility means undermining political and social stability, and this destabilizes the monarchy also. Within the context of the Early Modern Era, Candide looks like a deeply radical and subversive work of literature, and it is the overall subversiveness of this book as a whole, I imagine, which would have been its most dangerous feature—at least as far as the the Monarchies would be concerned.