I am trying to connect the data collected from Adobe Analytics to my local instance of MYSQL, is this possible? if so what would be the method of doing so?
There isn't a way to directly connect your mysql db with AA, make queries or whatever.
The following is just some top level info to point you in a general direction. Getting into specifics is way too long and involved to be an answer here. But below I will list some options you have for getting the data out of Adobe Analytics.
Which method is best largely depends on what data you're looking to get out of AA and what you're looking to do with it, within your local db. But in general, I listed them in order of level of difficulty of setting something up for it and doing something with the file(s) once received, to get them into your database.
First option is to within the AA interface, schedule data to be FTP'd to you on a regular basis. This can be a scheduled report from the report interface or from Data Warehouse, and can be delivered in a variety of formats but most commonly done as a CSV file. This will export data to you that has been processed by AA. Meaning, aggregated metrics, etc. Overall, this is pretty easy to setup and parse the exported CSV files. But there are a number of caveats/limitations about it. But it largely depends on what specifically you're aiming to do.
Second option is to make use of their API endpoint to make requests and receive response in JSON format. Can also receive it in XML format but I recommend not doing that. You will get similar data as above, but it's more on-demand than scheduled. This method requires a lot more effort on your end to actually get the data, but it gives you a lot more power/flexibility for getting the data on-demand, building interfaces (if relevant to you), etc. But it also comes with some caveats/limitations same as first option, since the data is already processed/aggregated.
Third option is to schedule Data Feed exports from the AA interface. This will send you CSV files with non-aggregated, mostly non-processed, raw hit data. This is about the closest you will get to the data sent to Adobe collection servers without Adobe doing anything to it, but it's not 100% like a server request log or something. Without knowing any details about what you are ultimately looking to do with the data, other than put it in a local db, at face value, this may be the option you want. Setting up the scheduled export is pretty easy, but parsing the received files can be a headache. You get files with raw data and a LOT of columns with a lot of values for various things, and then you have these other files that are lookup tables for both columns and values within them. It's a bit of a headache piecing it all together, but it's doable. The real issue is file sizes. These are raw hit data files and even a site with moderate traffic will generate files many gigabytes large, daily, and even hourly. So bandwidth, disk space, and your server processing power are things to consider if you attempt to go this route.