Use %%
to place %
in stringWithFormat.
So your code becomes:
NSString *urlString = [NSString stringWithFormat:@"https://api.xmltime.com/astronomy?accesskey=l1fMY6Om37&expires=2013-06-05T18%%3A00%%3A00%%2B00%%3A00&signature=12P2tr1MyD4NnLjqhWzc%%2BpsBKR0%%3D&object=sun&placeid=netherlands%%2Famsterdam&startdt=2013-06-04&enddt=2013-07-04&geo=0&isotime=0&lang=en&utctime=0&types=all", startDate, endDate];