You can use this script to delete all your Tweets. Even if they don't show up on your profile. But you need your Data Export for it to work. Because this automates the deletion, it may get your account banned. Not a bad outcome.
If the process is interrupted at any time, you can use the advanced options to enter how many Tweets have been deleted in the previous run to not start at zero again. The script will try to automatically detect if it was run before by calcualting the difference between Tweets in the file and the Tweet count on the profile. If there is a difference it will try to automatically skip that amount (+5% buffer). If you want it to start from the beginning, open 'Advanced options' and enter 1 instead of 0. It will the skip exactly one Tweet and not try to calculate an amount.
Instead of copy-pasting the script, you can install it as a userscript: greasyfork.org/en/scripts/476062-tweetxer (works with eg. tampermonkey browser addon)