Years ago you were able to mail in your ID info and business license, etc and Twitter would generally verify. However, since they have switched to a public company and need to generate revenue they now require "brands/businesses" to have a MINIMUM of $5,000 per month in Twitter Ads budget (which they are raising nearly every quarter) before issuing you an account executive in which they can get you verified. If you are famous from being a celebrity you can have your publicist send in the ID info as before, but for businesses they have made it extremely difficult and expensive to become verified.
This is just the experience I know from dealing with Twitter directly on verifications. If there is a member here who can make that happen through another avenue, then that is awesome!