I don't like colleagues that support the boss just because they want a promotion.
I don't like colleagues who back up the boss just for a promotion.
I despise coworkers that talk good about the boss just to get promoted.
同僚=colleague, coworker
ヨイショする＝support, back up, talk good about~, etc
昇進＝promotion
昇進する＝ to be promoted, to get a promotion
嫌う＝don't like, dislike, despise, hate
ヨイショするはいろんなニュアンスがあるので、基本的に上司を支持したり、褒めたりと言う意味として解釈しましたので、その場合ですと support, back up, talk good about, etc となります。
どうぞご参考までに！
日本 
