Spend a good amount of time preparing. Once you feel a bit confident, start giving interviews in companies that you wouldn't go or you haven't heard of, just for practice. After each interview, write down what went well, what didn't go well, topics that you need to read/practice/revise. Before the next interview, make sure to address the shortcomings.
Try to get offer letters even if you are not gonna go, helps in building confidence.
Once you are confident that you are able to comfortably solve hard questions in an interview setting, then go after the big players.