It's time to become the next singing sensation by becoming a K-Pop Singer in BitLife! You can both obtain the Singer career path, and get the K-Pop achievement by doing this correctly! This is actually pretty easy, unfortunately it comes down to a lot of random chance on whether you can get it quickly or not.
To become a K-Pop Singer, we're going to need to start a Character in South Korea, become a background vocalist, get promoted to Longer Singer, Singer, and finally to Lead Singer which allows us to become a K-Pop Singer! I've got more details below on how to accomplish all of this easily.
The most important part of this is to make sure you start your character in South Korea. The city doesn't matter, just make sure that's where you are born. Now, just age up through life without much consequence, because your school doesn't really matter. Once you graduate from High School you will want to start looking for the Background Vocalist job. You'll see a little microphone next to it. This is the entry level position to become a singer. If you don't see it, you'll just need to age up and look for it again next year. If you see any career that has "Record Label" near it, you can try to get that and it will hopefully encourage the vocalist job to appear.
Once you've got your Background Vocalist job going, make sure to work hard at it each year. You will eventually be promoted to Lounge Singer, Singer, and then eventually to become a Lead Singer! Once you've reached the top, just age through it and after about 5 - 10 years you'll get the K-Pop achievement! If you continue to maintain the career and age up more, after about 10 - 20 years you will get the checkmark for the Singer career!