How does Shaw attack upper-class society in Arms and the Man?

To begin with, the stage directions of Arms and the Man—which, in Shaw’s plays, are always highly specific—lay the groundwork by introducing the prominent Bulgarian Petkoff family as big fish in a small pond. The family, each in their own turn, relies on appearances whenever their concessions to reality fall short. This is, in itself, an entitlement of wealth. While everyone in the upper-class household—including the servants—must, to some extent, play by the rules of social propriety, these rules obviously only exist to favor those in power. The servants must stifle their own impulses to flatter their patrons until such time as they might need to exploit household secrets for leverage.
The daughter of the house, Raina—Calvary hero Sergius’s fiance—is particularly out of her depth during the Swiss ‘volunteer’ Bluntschli’s intrusion, and so she presents herself as a romantic figure, directly responsible for the proceedings yet naive about the male domain of mortal combat. Her behavior imitates that of the heroine in an opera. There’s a suggestion that Raina is unaware of the extent of her self-aggrandizing ways, living as she does, so much in the sway of mythology.
While Raina is guided by pretenses of cultural sophistication, the military hero Sergius is consciously operatic, a fatuous buffoon playing at chivalry. He acknowledges that his public role and high-flown position are a hierarchical social construct, a status display. But, in wooing the servant Louka behind Raina’s back, he loses composure over the nuances of his flirtation with a subordinate—a woman who should be grateful for his attentions but apparently considers herself his equal. This pretender claims that he contains multitudes as a man of the world but is confused. Is he the sexual aggressor in his entanglement with the maid, or is he the provoked?
The father and Sergius are each egotistical to the point that they can be easily hoodwinked by the women who ably gull them. Raina later understands that her “noble attitude” can be easily unmasked by Bluntschli, who is too straight-forward to indulge her posturing. But Bluntschli, as sympathetic as he is, is still Raina’s social inferior.

Raina: You have a low, shopkeeping mind. You think of things that would never come into a gentleman’s head.
Bluntschli: That’s the Swiss national character, dear lady.