The focus of the essay runs parallel to the SUBJECT of the given statement, and not the PREDICATE. What's the subject? The NOUN, "man," is a big hint. It's about man (in the non-gender neutral form that Cambridge apparently prefers), but what about him? The VERB, "is (at his best)," is the other hint. We're discussing Man being at his best, or, the Best of Man.
But this discussion will fill up volumes of encyclopaedia unless we set a context. In this case, the parameters fall within the scope of the PHRASE, "in times of crisis," which forms the PREDICATE of the given statement.
What follows, therefore, should be a discussion of the kinds of qualities that crisis brings out of us; an evaluation as to whether these qualities do indeed constitute our "best" attributes (best of what, exactly?); and perhaps some thought as to why and how these qualities become most obvious under stress, duress and imminent danger.
We could observe that people respond very differently from each other when facing crisis, and our best qualities don't always come to the fore. Depending on how people respond to crisis, they will be either victims, villains, or heroes. We villify self-serving, personal advantage-taking responses; we glorify and encourage selfless, generous, uniting kinds of responses; and... we light candles for the victims. It is in our memory, in hindsight and in the retelling of these crises as stories that we choose to highlight the best behaviour observed as an example for others to emulate in the face of other crises to come.
To focus the essay on listing the different kinds of responses we might observe from a range of different kinds of crises and suggest that we tend to "do our best" to overcome them just doesn't quite measure up to the full requirements of the question. Can pass, lah; but so-so only.
A tip for those of you taking your GP 'AO' this year: pay attention to your GRAMMAR so you can be certain of your focus of your essay. It'll make a difference to your grades. Trust me.