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I would focus on Python, Pyspark, and Scala if you want to work in the 'Advanced Analytics' space... it would also be helpful to have a general understanding of cloud architecture.
If you are thinking that the BI side of the house would be a smoother transition then I would look at Tableau and Qlik, perhaps some basics on Alteryx, SQL, etc.
Depends heavily on the company and role, but I would say at minimum:
-knowledge of stats (understanding of assumptions for regression, extensions to the linear model, basic experimental design)
-understand common ml techniques
-R or Python
-databases and SQL
For more tech based roles you will also want software engineering knowledge such as OOP, unit testing, common algorithms/data structures, etc
Can I have your job?
You do not need any skills at entry level, but tableau/power BI, Sql or databases in general will take you a long way and will suffice.