Remove the oldest tweets from your account using Twitter Archive Eraser, a .NET app for bulk tweets deletion using the Twitter archive.
More details about how to use this tool to wipe out your Twitter archive http://www.martani.net/2013/02/wipe-your-oldest-tweets-using-twitter.html
Update:
Ver 2.0 enables the use of the *.js archive files after the Twitter update the the archive structure.
You can download a working standalone version from here: Twitter Archive Eraser.zip Or, download the installer which will install all the required software (.NET 4.0 etc.): Twitter Archive Eraser Setup.zip
If you wish to buid the code yourself, you need to create a Twitter application here https://dev.twitter.com and provide the twitterConsumerKey and twitterConsumerSecret parameters in App.config.
<add key="twitterConsumerKey" value=""/> <add key="twitterConsumerSecret" value=""/>