The title the Master Farmer is unlocked by purchasing the 'farm deeds (+titles)' for 250,000 beans in the Farmers' Market which also unlocks the Granny, Potterington, and Grandpa/Grandma titles.
Purchasing 'farm deeds (+titles)' will prompt the following messages:
Granny P has retired - You now have full ownership of the farm!
Less importantly, you now have unlocked the title 'the Master Farmer'.
(Also some other titles, but let's not talk about those...)
This title changes according to the language of the server on which RuneScape is played, as shown below:
||[Name] der Meister-Landwirt / die Meister-Landwirtin
||[Name] le maître fermier / la maîtresse fermière
||[Name] o Agricultor Mestre / a Agricultura Mestra