How is Hamlet a revenge tragedy? critic's views
Since you've asked for critical responses, here are a few. Links to the articles in EBSCO appear below.
Abstract from the article, "Shakespeare's Hamlet":
Demonstrates that Hamlet purposely murders Polonius in the play 'Hamlet,' written by William Shakespeare. Description of the slaying in act 3, scene 3 of the play; Reason for the desire of Hamlet to kill Claudius; Other characters of the play who seek revenge against others.
Citation: Sterling, Eric. Explicator, Fall2001, Vol. 60 Issue 1, p2, 4
Abstract of "Shakespeare, Revenge Tragedy, and the Ideology of "Memento Mori":
Discusses how Shakespeare's works on revenge differ from the treatment of memento mori in his contemporaries' works. Displacement of orthodox religious ideology in English stage; Shakespeare's fidelity to tradition; Modes of expressing fascination with death; Perversion and subversion of religious discourse; Shakespeare's `Hamlet'; `Hamlet' versus other plays.
Citiation: Jacobs, Henry E. Shakespeare Studies, v. 21 (1993) p. 96-108.
Abstract of "The Case of Hamlet's Conscience":
Explores possible meanings of the concept of conscience in William Shakespeare's 'Hamlet.' Indications of Hamlet's conscience; Interpretations of Hamlet's problems; Depiction of revenge in the play; Popular treatments of cases of conscience.
Citation: Belsey, Catherine. Studies in Philology, Spring79, Vol. 76 Issue 2, p127, 22p; (AN 5242498)
In this drama, in initiation, Hamlet is chained in problems
caused by the unexpected marriage of his mother with his uncle. The
playwright’s mind is very swift and he makes destiny of all follow
revenge. he introduces the character of Ghost as the agent of death
that is in the shape of his father and Hamlet has to be believed.
The appearance of Ghost and disclosure of secret makes tussle
between Hamlet and Claudius. Hamlet has to take revenge. Its major
plot is only revenge. It runs through out the play. It is fact that
it causes of other sub-plot.
The main plot gives birth to the other sub plot. Polinus is the major supporter of the king. In this case, he works as spy and Hamlet, unfortunately, kills him. Apart from it, his daughter, Ophela, the beloved of Hamlet, too commits suicide. Lacerates appears for revenge of his father and sister. Again, we see Claudius is opportunist, uses Lacerates, but in kismet something is very different
Now Hamlet is opponent to Claudius and Lacerates to Hamlet. It means tussle is of those three persons. Hamlet tries his best but all is in vain. Both opponents try to murder each other but fate rejects and introduces delay.
At last, the fate provides occasion to all characters to deal with their enemies. Hamlet kills Claudius. Hamlet and Lacerates kill to each other at the end. The central plot is succeeded, for Hamlet manages to kill his enemy.That`s why it is a revenge tragedy.