This is a variation of Gokyo Shumyo, Section 1, Problem 81. White makes two eyes with one strike. There is an eye at each circled point.
Once the vital point has been played ( in the solution diagram) there is not much room for mistakes by White, so we will concentrate on what can go wrong at the first move.
The 1-2 point is another natural point to try, to make life, but Black can occupy , which is connected to the marked stone through a large monkey jump.