I don't understand "S/C problem at GRE"

English as a Second Language Preparation forum for the GRE® Test
1

Although recently _____, her reputation need no _____; her contribution to astronomy has been awarded by ~~~.

Answer : embattled, burnishing

But, I don’t know what means ‘burnishing’
I think that for example, “her reputation needs no contention etc.”
burnishing means???

2

sorry if this is a little late…burnishing means polishing

p.s. would sincerely appreciate it if you could reply to my post titled ‘weightage of GRE in admission process’