bust a gut

bust a gut (to do sth) AND burst a gut (to do sth) (to work very hard or to make a big effort to achieve something) — надрываться, корячиться; переламываться; надрывать себе кишки; биться из последних сил; вкалывать вовсю; ишачить; корпеть; из кожи вон лезть (чтобы добиться чего-л)

Example 1: It's kind of sad to see these kids bust a gut chasing a dream that will never succeed.

Example 2: I really bust a gut to get that report finished on time. (CIDI)

Example 3: I don't intend to bust a gut to get there on time. (CIDI)

Example 4: I busted a gut to get there the last time, and I was the first one there.

see also
[fall over backwards to do sth], fall over oneself
[go out of one's way to do sth]
[lay oneself out to do sth]
[pull out all the stops]
[bend over backwards]
[изо всех сил]

bust a gut (laughing) (to laugh very energetically ) — чуть не лопнуть от смеха; смеяться до колик; животики надорвать (от смеха); надорваться от смеха

Example 1: I bust a gut laughing at his imitation of the Queen. (CIDI)

Example 2: I bust(ed) a gut reading the story.

cf.
[crack up (over sth)]
[get a kick out of sth]
laugh one's head off
split a gut

[have sb in stitches]
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Etymology:
based on the idea that extremely hard physical work or laughter could damage your gut (stomach)

(The word gut is considered impolite in some circumstances. Bust is a non-standard form of burst.)