Learn English – What does the phrase “Real mature with that one” mean

The origin for this phrase is likely theatrical: "Hard act to follow"

Before television, people used to watch Variety Shows at theatres for entertainment.

One of the key characteristics of such a show is that as the show progresses, the acts should get better and better.

The headline act goes on last because they are so good that they cannot be followed.

So if someone cracks a great joke or tells an amazing story, the expression, "Follow that!" is an imperative or challenge to improve on the joke with an implied assertion that you cannot because it was so good.

If you are on a bill of performers and the preceding act is better than yours then there is no greater hell; for you or the audience.

It's a sarcastic comment, intended to insult, which is why the fight ensued.

As with all sarcasm, it “depends for its effect on bitter, caustic, and often ironic language that is usually directed against an individual” [MW]; in this case Tikakeyev implies Koratygin is anything but a good example (of whatever it is) by saying exactly the opposite of what he means. This particular remark is entirely idiomatic English.

It needs the right tone of voice to be fully effective, but the exclamation mark is helpful.