Twitter folks have previously stated that they do not delete tweets, for users and it's up to the individual to do so, if they please. To be honest, I couldn't agree more.
However, I have the answer you've been looking for. Delete All My Tweets allows you to delete a number of tweets at a time and can be a long process (depending on your tweet count) but this tool actually works.... and my friend, I have tried many!!
For iOS users, try....
DELETE TWEETS: DLTTR, removes ALL available tweets, but Twitter has some limits, and the counter can be not zero. Check the FAQ in the application!
★ World best tweet deleter
★ Can delete the latest tweets by an hour, day, week, month, year or all of them once
★ Can help you if you wrote anything you regret about and seconds matter, or drunk tweets you cannot remember at all
★ Specially designed interface with a magic big red button and authentic sound
★ First time in Applifto apps – Help mode!