The two permissions that you would have to start looking into are CreateApplicationVersion and UpdateEnvironment. However any IAM permissions would require your developer to have AWS credentials, either from his/hers account or yours.
I think it would be easier and more straight forward to create simple CodePipeline with Elastic Beanstalk action provider. So your developer would upload new code to some repository, S3, github, gitlab, CodeCommit, and the upload process would trigger it automated deployment in Elastic Beanstalk.
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