You can download all the languages from a localization project in two ways.
Export all languages with the API
To export the localized strings from all the languages in your POEditor project with the API, you first have to use the languages / list method. Then, for each language, you need to send a request containing the project ID, language code and format to the export endpoint.
Export all languages with GitHub, GitLab, Bitbucket or VSTS integration
If your project is integrated with a code hosting platform, you can also export all the languages at once.
One way to do this is to select all the linked project languages and press the Export button at the bottom of the integration page.
You can also create a export_terms_and_translations Webhook for each linked language and put them in a script that would run them all at the same time.