This is the 3145th most frequent Russian word.
личными
The Russian word "личными" means "personal" or "private" in the instrumental plural form.
In this sentence, 'личными' refers to 'personal', indicating that the impressions belong to him and are subjective.
Он поделился личными впечатлениями.
He shared personal impressions.
Here, 'личными' is used to describe 'achievements' as her own and individually attributed to her.
Она гордится своими личными достижениями.
She is proud of her personal achievements.
In this context, 'личными' refers to 'methods', specifying that they are of individual origin and approach.