How can I generate a plot like the following in R.

It shows the percent of transactions (x) for a given response time (y), see my own answer below for my own go at it.
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Methinks you want a plot of an empirical cumulative distribution function.
So take a look at the documentation for
ecdf()as well as the more featurefulEcdf()in the CRAN package Hmisc.Hmisc Ecdf example:
ExecTmarray of execution times,HttpProvCallarray of time it took to call downstream system and we compare the time we spend with the downstream system with percentiles