Measure highest number of simultaneous visitors via Google Analytics

You can estimate that using this formula:

Simultaneous Visitors = Hourly visitors * Average Time Spent on Site (in seconds) / 3600

Hourly visitors can be easily found in Audience Overview and Average Time Spent on Site through "select metric" on the same view.

As Samwise has said, it's entirely impossible to see the number of simultaneous visitors historically using Google Analytics.

Your only two options (if you insist on using GA) are to use the live view tab which only shows data from the past 30 mins (not ideal) or simply report on the number of visitors per hour in standard reporting (again not exactly what you're looking for)

I have never used the service that Samwise linked to but it's worth a shot!