Introduction 

    It is very nice to meet you, Mr. XX and Ms. XX. Let me introduce myself. first. 

[the first you wrote is correct, but I think it sounds more natural without it. If you really want to include it, I think it sounds more natural to say "First, (please)let me introduce myself." Depending on how formal you want to be, you can put in "please." The east coast of the U.S. is much more formal than the west coast, so if its in New York maybe add in the please.] 

     I'm Becca, I came come from Mainland China, and have legal backgrounds in both Mainland China and Hong Kong. I passed the Judicial Exam of the PRC three years ago in the same year when that I came to Hong Kong to pursue my further education. I graduated from XXU in 2012 with a masters degree in Law.
     Right after I graduated, I received an excellent offer from AA law firm in Shenzhen, which is one of the largest law firms in mainland China specializing in the capital market business. I worked there for half an year. [y is sometimes a vowel, but in English you never use "an" before a word starting with "y", always use "a".]  year. In this position, I had the chance to follow several IPO or M&A projects. My role was to conduct the due diligence work for the projects, conduct legal research and draft due diligence reports.
     The reason why I came to Hong Kong is because Hong Kong is more international, and has more exposure to the global market. I would like to step out of my comfort zone to have a more challenging job. ["would like" sounds better than "just want" here since it is more formal. "just want" is very informal.] 
     I am now working in the BB Company as an in-house legal officer. BB company has been listed in the CC Securities Exchange for 20 years. It is a holding company with 3 subsidiaries in Mainland China, and is still trying to expand their its business in Mainland China. I report directly to the Chairman of the group. Because of the size of the company and the Chairman's high level of experience as an accountant in this area, I am the only one in the company that deals with legal affairs. I have the chance to deal with all the legal tasks works [other than in "public works projects" we don't really use "works" often as a noun like you've used it here. Usually "tasks" instead.] in the group, such as drafting contracts, follow up with litigation cases, conducting basic due diligence in the company's acquisition [I'm not 100% of your meaning here--the acquistion of another company by the company you worked for, or your company's work helping other companies on acquisitions..maybe check your wording here. As it is more or less ok but unclear. We often will not use acquisition alone, instead I see said more often "merger and acquisition" together, but this may be a specific business technicality..] My work also includes the corporate part of the company's work, such as drafting minutes, announcements, preparing for share issue or share transfer documents, general meeting documents, replying [all the verbs in your list have to match each other. so since you used "drafting" and "preparing", you also need to use "replying"] to the ASX inquiries, etc. 

     The reason why I am considering to changing a jobs is that the company that I am currently working for is not very dynamic. company is not going through some changes. Of course, they have expressed that they would like [more formal than "want me"] want me to stay. But [Best not to start a sentence with "And" or "But"] However, I think if there exists is a better opportunity chances [it is better to use opportunity here I think. "chances" is very colloquial--i.e. not used in writing as much] for me, I would like to leave ["go" is correct but very informal, so "leave" is better. But I think what would sound the very best is "I would like to try something new"] go because I would like want to work in a bigger larger [larger is more formal than bigger] and more professional team. And Also,  [English speakers do do this in informal writing and speaking, but it is usually taught to us in school that you should not start a sentence with "And" or "But"] working in a law firm is always my goal.