The BBC investigated Ryanair's claim and found some problems with them. The main problem being that the figures are those of Ryanair without any independent verification.
Ryanair claims that its figures include data from the Association of European Airlines. According to the BBC report, the AEA has not published any figures since 2009. Secondly, some 200 European airlines are not members, including Ryanair itself.
The article presents information from independent wibesite, flightontime.info, which measured performance at 10 UK airports and came up with a figure of 83% on time at those airports.
Overall Ryanair's claim could be true but we only have their word for it.