perfect

Thank you for editing, I tried to curry favor with the boss by working extra hours and completing tasks ahead of time.

Perfect. Just a tiny edit: “…ahead of schedule” or “…ahead of time” would sound better here.

I would not say more elaborate, I would say “curry favor with” is less insincere than kissing up. For example, you can “kiss up” or “suck up” to a boss by saying things you think he wants to hear, even if you don’t mean them. It’s insincere and transparent. But “curry favor with” might be to do things that benefit your boss, hoping he/she will approve. They are legitimate things that in addition also win you their respect or favor.

Great! You might say, “We have a presidential election coming up this year.” That means it’s coming in the near future. And second, you can simplify the sentence by saying, “Some companies are beginning to curry favor with…”

“Curry favor with” typically happens over an extended time (it’s like a habit), so you don’t need to say “continually curry favor with.” Check this out with a few small revisions: “In most cases, it’s not enough to curry favor with a boss to get a promotion or raise. Professional skills and knowledge usually play a bigger role because you cannot fully rely on flattering people in business situations.”