go to https://twitter.com/your-username, and enter the following into the developer console (F12)

twitter-delete.js

// Delete tweets
for(var i = 0; i < document.getElementsByClassName("js-actionDelete").length; i++) {
  var tweetToDelete = document.getElementsByClassName("js-actionDelete")[i]
  if (tweetToDelete) tweetToDelete.childNodes[1].click();
  document.getElementsByClassName("delete-action")[0].click()
}
// Delete retweets
for(var i = 0; i < document.getElementsByClassName("ProfileTweet-actionButtonUndo").length; i++) {
  var tweetToDelete = document.getElementsByClassName("ProfileTweet-actionButtonUndo")[i]
  if (tweetToDelete) tweetToDelete.click();
  document.getElementsByClassName("js-close")[0].click();
}