Solution 1:

A possible idiom is "trumping [it] up". From Merriam-Webster:

Definition of trump up

transitive verb

1: to concoct especially with intent to deceive : fabricate, invent

2 archaic: to cite as support for an action or claim

Solution 2:

Full of hot air

A person who is full of hot air is a person who talks a lot but whose words carry no substance. This does not always refer to outright lies (It can, of course.), but if not, the claim in question is so unrelated, confused, exaggerated, or misleading that the person may as well be lying. This phrase is informal, dismissive, and somewhat insulting.

The phrase has variations on "hot air":

  • it
  • bull
  • Expletives referring to excrement
  • A combination of the last two: "bull [expletive]"
  • beans (This can also mean that something is lively, though. So only use if the context makes it clear you wouldn't be saying that.)

Naturally, the versions containing curse words express greater discontent with the person.