Professional services seems difficult to find... almost as though Taiwanese favors chabuduo tradesman (probably because they're cheap).
Muratic acids (Hydrochloric Acid) is readily available in Taiwan, both the diluted and the fully concentrated version... they work wonders on any calcium based scums and in my experience really whitens the grout. That and a pressure washer should deal with most dirt.
Do buy the dilute hydrochloric acid though, as the full strength stuff is VERY corrosive and while you can dilute it yourself, it is unsafe unless you know how to do it. Remember what your Chemistry teacher told you, always ADD ACID TO WATER!!!
Sulfuric and Nitric acid is also readily available in Taiwan in chemistry stores, but you do not need them to clean tiles... they are also highly corrosive... do not use them for cleaning... they are far too strong and fairly dangerous to work with. They're better used as battery acid and possibly making explosives....