There are different rules for NG vs AR vs AD for promotions so some of these may not be pertinent to your particular environment however, in general, for enlisted, the best way to advance in their careers is:
college credit or distance learning for promotion points (ACES)
excellent PT scores
marksmanship scores
Excellent NCOER/SNCOER (evaluation reports)
NCO professional development- WLC and the like
Other army schools such as Airborne /Air assault/ expert field medic or possibly even secondary MOS schools
Time in service / time in grade
Awards / ribbons such as ACOM, AAM, bronze star, purple heart, good conduct, combat medic / action badge, etc. Even certificate of appreciation may count.
The majority of these things are self-driven items and unfortunately, there's not a whole lot you can do to facilitate an individual's career advancement other than provide positive mentorship, encouragement, and ensure the unit administrators are getting their jobs done effectively.
**former NG 68W NCO**