bad, grave, great, terrible
one of the worst insults you can throw at somebody

final, ultimate
To call a woman a girl is the ultimate insult.

calculated, deliberate (esp. BrE)
direct (esp. AmE)
personal

hurl, shout, throw
They were hurling insults at the police.

mean sth as
I don't mean this as an insult, but I think the team would play better without you.

take sth as
I meant it as a bit of constructive advice, but he took it as a personal insult

endure, suffer
Foreigners have to suffer constant insults from the local population.

exchange, trade
The two groups of fans exchanged insults.

fly
Insults were flying back and forth.

insult to
It was an insult to his wife.

add insult to injury
Then, to add insult to injury (= to make things worse), they told me I couldn't get on the flight.

an insult to your intelligence
The questions were a real insult to our intelligence (= because they were too easy).

publicly
He was dismissed for publicly insulting prominent politicians.

be insulted, feel insulted
I felt deeply insulted that she hadn't asked me to the meeting.

Insult is used with these nouns as the object:
intelligence