I based my changes on my gut feeling of how it sounds. 'at' is used when describing your location, while in is used to describe where you are within that location: "I'm at MUJI's in the women's department".

I took a part-time job as a shop assistant at MUJI last year. Have you heard of that Japanese brand?
It was my first try taking up a part-time job. Becasue of the heavy school load at the end of the semester, I asked for leave this January off. Today was the my first time back work in  at MUJI's shop again this year.

you can't use the word 'again' because you added 'this year' and its your first time back this year. 

Unfortunately, today was very boring...There were only a few customers, and most of the time I was just standing in front of the fitting-room. The worse worst thing was that some colleagues whom I am was familiar with quit the job some days ago. I felt a little lonely and missed them.

Saying 'was familiar' suggests you are no longer familiar with them anymore.

Although I don't like this these kind of jobs, I appreciate what I've learnt learned and experienced. In addition, it has advanced my social skills. I'm really a shy person and I was afraid of answering strangers' calls...But now it is gets getting much better.

This turns to these when your talking about more than 1. The word learnt is used very rarely in speech, in the US people use learned. Since its a continueing process use getting instead of gets. 

Besides, I love MUJI's design concepts very much. Its goods are simple, useful and qualified high quality.
Its designers - 原研哉 and 深澤直人 are my favourite designers as well. I've read some of their books. Their thoughts are profound and I think I should learn from them.

Finally, I hope I can insist on working...Good night everyone.^^

Back from work.

I took a part-time job as a shop assistant in MUJI last year.Have you heard of that Japanese brand?
It was my first try to take up a part-time job. Becasue Because (I forgot to say that also "because" is frowned upon as a way of starting a sentence, you can say "It was because" of heavy studies at the end of the semester, I asked for leave this January, and today was my first day back since then. The blue is just a suggestion) of heavy studies in at the end of the semester, I asked for leave this January, and today was the first time back to working in MUJI's shop again this year.

Unfortunately, today was very boring...There were only a few customers, and most of the time I was just standing in front of the fitting-room. The worse thing was some colleagues whom I was familiar with quit the job some days ago. I felt a little lonely and missed them.

Although I don't like this kind of jobs (since you wrote this and kind, I assume you mean singular so there shouldn't be an s in jobs), I appreciate what I've learnt (this is correct learnt, just for you to know, learned is more commonly used than learnt in the U.S.) and experienced from it. In addition, it advanced my social skills. I'm really a shy person and I was afraid of answering strangers' calls...But now it gets much better.

Besides, I love MUJI's design concepts very much. Its goods are simple, useful and qualified.(Qualified?) 
Its designers - 原研哉 and 深澤直人 are my favourite designers as well. I've read some of their books. Their thoughts are profound and I think I should learn from them.

Finally, I hope I can insist (I don't think you mean insist, it means like forcing. So I think don't think you mean to say that you hope to keep forcing yourself to work) on working...Good night everyone.^^