The principal irony in "Shooting an Elephant" is that although the story is a picture of colonialism, in which the British have placed themselves in charge of an Asian country, Orwell himself, as a British policeman, finds himself "controlled" by the crowd of Burmese people. It is as if the power dynamic we would expect to be in force has been reversed. This, at any rate, is the situation as Orwell perceives it. His major point is that the white man destroys his own freedom when he turns tyrant over other people.
The case of an elephant gone berserk seems at first to be a straightforward one, but because the animal's violent behavior is only temporary (due to an attack of "must"), Orwell's judgment in the moment is that there's no longer any need to kill it. The beast can presumably be recaptured by its owner without further mayhem. However, a huge crowd of "natives" has gathered, and Orwell, the "white man with the gun," feels egged on by them to do something decisive, even if it's wrong, so he shoots the elephant and does so inefficiently, with the result that shot after shot is required and the animal takes a long time to die. The death throes of the elephant are a metaphor for the whole dysfunctional dynamic that exists in a colonized land between the conqueror and "the natives."
Arguably, however, a secondary irony exists within Orwell's perception of the incident. As a man with progressive feelings, he knows that British imperialism is wrong, but his own personal attitude toward the Burmese, as he acknowledges himself, is a largely negative one. He describes being tripped up on the football field and being laughed at by the Burmese players, and he decries the fact that Buddhist priests are standing about "having nothing better to do than jeer at Europeans." It is ironic in the extreme that Orwell seems to regard himself as the principal victim in all of this. He makes a good point about the white man as a conqueror ironically destroying his own freedom, but even from his perspective of greater maturity in writing about the incident years after it has taken place, there is an element of narcissism in his viewing himself as more of a victim than the colonized people, whose freedom has been taken from them on a continuous basis and not merely in an isolated occurrence.