Aside from collecting critters to complete the Pokedex, another hobby most Pokemon GO trainers have is to collect medals, which are awarded after you complete or catch a number of Pokemon. One of these is the Gold Dragon Tamer Medal.
To answer the easiest way possible, all it takes for you to become a Gold Dragon Tamer is to catch 200 Dragon-type Pokemon, such as Dratini, Dragonair, and Bagon. Popular dragon-type trainers in Pokemon lore are Lance, Clair, and Drake.
Before you become a Gold Dragon Tamer, you become a Bronze Dragon Tamer which requires catching 50 dragon-types. After that, you become a Silver Dragon Tamer wherein you need 100 dragon-type Pokemon. The most important question here is how long does it take for someone to become a Gold Dragon Tamer or how long does it take for you to catch all 200 dragon type Pokemon?
It is very difficult because, at the moment, there are only three dragon-type Pokemon and getting one requires a high level. One Reddit user named NorthernSparrow gave an estimation/calculation based on his own experience. He himself is not yet a Gold Dragon Tamer but he has already several Dratini being a Level 33 Pokemon GO player. He caught two of his Dratinis while hatching one 20-kilometer egg. According to him, he acquired all three dragon-types in a span of 111 days or 37 days for each Dratini.
Earlier this month, he caught more dragon-types when he visited New Orleans giving him a total of 37 which leaves him 163 more in order to achieve the Gold Dragon Tamer Medal. So he calculated how long it would take him to get that medal if he continues playing in the town where he lives.
He said suppose you play 2 hours a day and you walk 10 miles per day with 9 incubators running (just as he did with his first three), he will be able to acquire all 163 dragon-type Pokemon in 16 years and 6 months. Let's say you're 18 years old now, you'll become a Gold Dragon Tamer when you turn 44 years old. Good luck and happy Pokemon hunting.