Is it necessary to completely change the direction of the face to avert one's gaze from a girl, or is it sufficient to change the direction of the sight while a part of the eye still catches a glimpse of her?

Your question involves overthinking, and we hope it is not due to whisperings (waswasah). The lowering of the gaze commanded in the Quran is to avert the gaze from that which is unlawful to look at, so that the eye does not fall upon it and temptation occurs. This is as stated in the hadith of Jarir ibn Abdullah: "I asked the Messenger of Allah, peace and blessings be upon him, about an accidental glance, and he commanded me to avert my gaze." The meaning of averting the gaze is to direct it right or left so that the avoidance of temptation is achieved.