One way to achieve the highest register on the oboe is to make sure you are opening the half hole enough. You can get to the desired upper register by opening the hole in the side of the air column that is close to the mouthpiece. Oboe design includes different holes for achieving the upper register.
To achieve even higher notes, a second register key is utilized. This key is used along with the first register key. This second register key closes the first hole. It opens one that is closer to the mouthpiece and assists in getting to those higher notes.
These are the mechanics and the engineering put in place by the manufacturer to help musicians get to the highest register on the oboe.
However, the musician has his or her role to play in getting to the highest register on this instrument. The player must work in concert with the oboe's design to achieve these top-level notes. It's important to make sure you are not biting the reed too much. You can place your teeth on the reed and higher notes require this, just be careful not to bite down too hard.
In addition, ensure you are producing strong and consistent air support/flow. If you do not pay attention to this requirement you will find that the upper register notes are flat and unstable. Unstable higher notes will tend to slip back into the lower register or quit sounding at all.
Furthermore, make sure you are not opening your throat too much. Moreover, check that your embouchure is appropriately tight, not loose. Just like playing the trumpet, the embouchure of your lip region must be strong and made tight enough to produce a quality robust air flow that contributes to achieving the higher register. It is advisable to use the appropriate pressure from your embouchure on the reed; this method disturbs your playing less.