You need to download your Twitter Archive. or You can use one of the Twitter management Tool. If you want to delete them then second way is more handy for you.
Let me first explain how to get your Twitter archive, then the other way.
1 Go to your Account settings by clicking on the more icon in the navigation bar, and selecting Settings and privacy from the menu.
2 Under the Account section, click Your Twitter data.
3 Enter your password under Download your Twitter data, then click Confirm.
4 Click the Request data button. If your Twitter account is connected to Periscope, you’ll have the option to Request data from Periscope as well.
5 When your download is ready, we'll send an email to your connected email account. From your settings, you can click the Download data button under the Download data section.
6 Once you receive the email, click the Download button while logged in to your Twitter account and download a .zip file of your Twitter archive.