Yes, you can definitely verify your Instagram profile with a blue tick but for that, you need to be a very sound personality among the folk. Unless and until you aren’t a public figure, a celebrity or a global brand it represents your account will not be verified by Instagram.
The blue tick which appears next to an Instagram profile and account name in the search is basically a badge which shows that the account is verified and according to Instagram privacy policy it is given to people or brand page which are publically sound.
Instagram provides blue tick so that the accounts on Instagram which have a high range of likelihood and followers so that it gets easy for people to search authentic people and business pages on Instagram easily.
An individual cannot transfer, sell or advertise a verified badge, and doing so may result in badge removal or termination of your Instagram account.
For more details, you can visit: Help.instagram.com