"Critically analyse" is one of the standard phrases you get in essay titles. The difficulty of carrying out a successful critique depends on the subject at hand and topic of the essay. It does get easier with time, and you can either attack the foundations of whatever premise you're considering or the consequences, as well as particular weak spots that may have grabbed your attention.
That said, DON'T overanalyse. Pick maybe a maximum of three gaping holes that you can find and attack them solidly. If you can undermine an argument on two solid fronts rather than present a miscollated hodgepodge of minor points, you'll have demonstrated that you have critical analysis down to a tee.
It'd also help if you told us what you were writing on so that we can give more relevant advice. Good luck!
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Furry is the leader of his own cult, the "Furballs of Doom". They sit about chanting "Doom, Doom, Doom".
(From a random shot in the dark by SirLance)
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