If you have ArcGIS Pro try the Feature Class to Feature Class geoprocessing tool with the environment setting Maintain Attachments set.
You could also try to go the REST API interface in ArcGIS Online and Create a Replica. This could also be done with the REST API and an HTTPCaller.
I wrote an article about it, which you can find here.
@heartlacey
It seems there is still no direct and one-tool way to read and write AGOL Feature service with the attachments into a geodatabase. This is primarily due the way the geodatabse stores feature classes with attachment, i.e. using 3 different tables: feature class, attachment table & a relationship class.
I found a template in the following link that helped me achieve this. Scroll to the bottom of the link and download the zipped file. You just need to customise the setting to meet your needs. The workflow works really well.