Starting at the 1-2 point to prevent White from linking up, and simultaneously occupying a vital point, is pretty obvious.
... Black recaptures at !! If White now connects her stones at , creates shortage of liberties. Note the liberty at the circled point, without which Black would not be able to execute this tesuji, since would be self-atari.
If at here, is just in time to capture the lot without ko. Once again the circled liberty is necessary to make that possible.
If White takes the other 1-2 point, and destroys the eyeshape with , then makes life. at a dies in gote.
Question: As Black has outside liberties, after at a, can't Black capture White's 4 stones and live?
Answer: yes. This is in the realm of endgame, and correct timing of plays, rather than life and death. If white plays at a too early, black should ignore it and take sente to play elsewhere. Then it might turn into seki, if the outside liberties get filled before black comes back to capture the white stones.
Answer: Yes. Ambiguity removed.
If Black fails to see the tesuji, and falls for the temptation to occupy both 1-2 points instead, creates a ten thousand year ko. Note: in case the tesuji mentioned above doesn't work, since the liberty at the circled point is filled, this is Black's best option.
The only other option we have to investigate is here: it also prevents White from linking up, and if it worked, it would perhaps make more points than the correct answer. We will make this another problem: Gokyo Shumyo, Section 1, Problem 20b.