There may well be a double meaning to "Termagant" in Act III, Scene 2. For, while the origin of the word Termagant is unknown, it
does not seem to derive from any actual aspect of Muslim belief or practice, however wildly distorted [Enotes] even though it is interpreted as such in the translated text.
So, perhaps, in Hamlet's instructions to the players as he instructs them to be cautious about tearing an emotion to tatters, he cautions them not to be like the literal termagant, a ranting bully or a shrewish and demanding woman, much like Rip van Winkle's wife, Dame van Winkle, because he does not wish to alarm King Claudius and, therefore, arouse suspicion of Hamlet's being involved with the play. Hamlet hopes to subtlely unnerve Claudius; when Claudius asks Hamlet if the play is designed to offend, Hamlet quickly assures him
No, no! They do but jest, poison in jest; no offence i'
Clearly, Hamlet has had no intention of arousing suspicion in Claudius. Instead, he plays subtlely upon the conscience of the usuper.
In Act III, scene ii, of William Shakespeare's Hamlet, Hamlet states the following:
I would have such a fellow whipped for o'erdoing
Termagant. It out-Herods Herod. Pray you avoid it.
Here, Hamlet is instructing the Players on how to deliver the speech he has prepared. In his reference to both Termagant and Herod, he is alluding to the fact that one should not rant on about unimportant things (like the historical Herod and Termagant).
This said, the literal meaning of the word termagant refers to a Muslim god who is unrecognized by Christians. This god is known to be one who is characterized by his overbearing and violent nature.
The irony lies in the fact that Hamlet states that one will be whipped for overdoing Termagant. Given that Termagant is already known for his rants, overdoing a rant would tend to be overkill.