Nature metaphors often appear in The Tempest. In Act 1, Scene 2, Prospero describes Antonio as "ivy":
[...] he was
The ivy which had hid my princely trunk
And sucked my verdure out on't. Thou attend'st not.
Here, Prospero metaphorically refers to Antonio as the ivy that hid his (Prospero's) "princely trunk." In other words, Antonio acted like a vine that grows up a tree, hides it completely, and sucks out all its vitality. When Prospero devoted himself to studying, Antonio acted much like an invasive plant species and took over his dukedom.
This might seem like a strange metaphor. Given Prospero's mastery of nature, it seems even stranger that he might choose to describe his treacherous brother this way. But given that the betrayal happened before Prospero obtained his magic on the island, it makes sense. This metaphor makes Antonio's actions seem inevitable and unstoppable; perhaps Prospero uses it to demonstrate that there was nothing he could have done to stop it. It was almost a natural occurrence, more annoying than threatening, that can be reversed when Prospero sees fit. By comparing Antonio's actions to a natural overgrowth of an invasive plant, Prospero implies that the loss of his dukedom was an inevitable event that he had little power to stop.
Shakespeare uses the theater as a metaphor for life in many of his plays, and The Tempest is no exception. In Act 2, Scene 1, Antonio describes his harrowing experience of the tempest:
We all were sea-swallow'd, though some cast again,
And by that destiny to perform an act
Whereof what's past is prologue, what to come
In yours and my discharge
Despite the terror he faced in the storm, Antonio emphasizes the control he and Sebastian have over the future; he insists that it remains in his and Sebastian's "discharge." The metaphor presenting this situation as if it's an act in the theater shows that Antonio believes in his own success—the word "destiny" reinforces the idea that the play has already been written and that Antonio merely acts out his predestined (or pre-scripted) role. Of course, Antonio's character remains unaware that he exists solely within a play, which provides a delicious bit of humor for the (real) audience.
The tactic of referencing plays within plays is also known as metaperformativity and echoes conversations in As You Like It ("all the world's a stage") and Macbeth ("a poor player that struts and frets his hour upon the stage"). Evidently, Shakespeare thought the theater served as a great metaphorical representation of life itself.
The Tempest brims with ingenious metaphors. In Act 2, Scene 1, for instance, Antonio uses metaphors and an instance of personification in his effort to convince Sebastian to murder his brother, Alonso. Speaking about Alonso, Antonio says:
Whom I, with this obedient steel, three inches of it,
Can lay to bed for ever; whiles you, doing thus,
To the perpetual wink for aye might put
This ancient morsel, this Sir Prudence, who
Should not upbraid our course. For all the rest,
They'll take suggestion as a cat laps milk;
They'll tell the clock to any business that
We say befits the hour.
The phrase "obedient steel" personifies Antonio's knife, framing it as loyal to Antonio—and, in turn, showcasing Antonio's thirst for control. Antonio emphasizes the fact that his own weapon obeys him, even though it never had a choice. "Perpetual wink" metaphorically refers to the eternal sleep of death. It sounds cheeky, but it has grim implications. Similarly, "ancient morsel" refers to Gonzalo, because Antonio considers him to be an old piece of flesh. This is also a very dehumanizing epithet that helps distance Antonio from the emotional fallout of his suggested plan for him and Sebastian to murder Gonzalo and Alonso. On the whole, Antonio seems very enthusiastic about the potential murder, but his evasive language implies his desire to distance himself from wrongdoing. For instance, he does not say "my knife"; he says "obedient steel," as if he doesn't want to specifically name his weapon. Likewise, "perpetual wink" is a much softer term than "death."