Many people in Singapore have tattoos, both men, women and children. It's common to see tattoos on old women's ankles-so don't worry.
The only thing to consider is when you are looking for a job, but I don't think you will be stupid enough to go to work barefoot and deliberately show people that you have tattoos. You should be practical at work or something. It won't be any trouble to be seen by classmates-
To apply for a visa, as long as you bring what you need, dress appropriately and talk appropriately, it is generally easy to apply for a study visa:) Good luck!