“在某人手下工作”，直接说：work under sb.；用work for sb.也可以，因为“为某人工作”，意味着雇佣和被雇佣关系，同样表达出“在某人手下工作”之意。例如：

▲ work under somedoy:

1. I am the new manager and you will be working under me. 我是新任的经理，你们将在我手下工作。

2. Many men still don’t like working under a woman, and would rather have a male director. 许多男人仍不愿在女人手下工作， 而愿意让男性当自己的上司。

3. He works directly under the minister. 他直接在部长手下工作。

▲ work for somedoy:

1. The people who worked for her all admired her cleverness and courage. 在她手下工作的人都很佩服她的机智和勇气。

2. The people who worked for him lived in mortal fear of him. 在他手下工作的人对他怕得要死。

3. It was ridiculous that Caldwell, who used to work for me, was suddenly above me. 荒谬可笑的是，过去一直在我手下工作的卡德尔，竟然突如其来地成为地位高于我的人。

 关于你的两个句子的翻译：

1. 在女老板的手下工作不容易的。

It is not easy to work under a female boss.

2. 在像您这样的老板手下工作很开心。

I am very happy to work for a boss like you.