“Corrupt” would almost certainly be a statement of opinion, so not actionable in the US. A lot more detail would be necessary for this to be defamation.

“Judge XXXX has taken millions in shadow bribes and has consistently ruled for the wishes of his/her benefactors. There has been a history of being reversed on appeal proving their bias. Also I watched them kick a puppy.”

Then, obviously, these things would have to be false. Even then, the bar is pretty high. There are exceptions both ways on this, but as a general guideline, if the public knows a person’s name (judge in a high profile case, for example) they are probably classified as a public figure. The rule there is one of “actual malice” which isn’t exactly what it sounds like, but it’s the highest bar for defamation cases.

The speaker would have to say something factually false, knowingly or with no regard for the truth. Giuliani, for one recent example, was found guilty of defaming the Georgia election workers, because he went into great detail about his false claims, and he was told repeatedly that thise claims were false, but he kept going.