「スキルアップ」は英語で何て言うの?

I asked someone the other day "why are you studying English". The person's answer was something like スキルアップ.

× I want to skill up.
○ I want to increase my skill at English.
○ I want to improve my English. (more natural)

In Japanese, we can find many cases of __(n)__ アップ which are not real English, like:

レベルアップ
プライスアップ
バストアップ (this seems to be a popular search at Google)

None of these are real English. In English, we never use __(n)__ up, and "skill", "level", "price", and "bust" are all nouns.

However, we do have many phrasal verbs using up.

__(v)__ up

For example:

• get up
• stand up
• fill up
• grow up

I was sitting in a Starbuck's across from a McDonald's and saw McDonald's latest campaign: the Texas Burger. That's what you're looking at in this photo.

I'm from Texas, so it's kind of funny to see Texas used as marketing. Since I'm a vegetarian, I'd never eat one. The gimmick is that it's supposed to be filling, right? Sure, it might fill your stomach up, but it will also fill your veins up with cholesterol. You're better off passing up the Texas Burger.

(definitions from Eijiro on the Web)

fill up

穴・隙間｛すきま｝・空所｛くうしょ｝を〕満たす、充填｛じゅうてん｝する、ぎっしり詰める、いっぱいにする、〔車を〕満タンにする、〔池を〕埋める、〔食欲｛しょくよく｝を〕満たす At this rate, our landfills will be filled up in no time. : この調子でいくと埋め立て地はすぐに満杯になってしまう。

pass up〔機会｛きかい｝・取引｛とりひき｝などを〕逃す、逸する
・How could I pass it up? : 見逃す手はないでしょ？
・That's too good of an offer to pass up. : そんなおいしい話、逃すわけないだろ。
・This is an opportunity I can't pass up. : これは見逃せない好機です。

• 静脈 (じょうみゃく) (n,adj-no) vein; (P); (definition from Edict)
• コレステロール (n) cholesterol; (P); (definition from Edict)