A Protected Market
The player’s country:
With Mare Nostrum
With Mare Nostrum, 100 diplomatic power can be spent to increase mercantilism by 1%, which makes the achievement easy. One very simple (if somewhat tedious) method is to play as Tidore or Ternate, eliminate the other, and then play on speed 5 while doing nothing but increasing mercantilism until you get the achievement. You are sufficiently isolated that being behind on technology won't be an issue before you get the achievement. Setting a diplomatic national focus and hiring a strong diplomatic advisor will speed things up. Using administrative and military power to develop your province will ensure you can always afford a maximum level of advisor and a strong navy of heavy ships that can protect you just in case any other country does become aggressive.
Another option is Ryukyu, who starts as a tributary of Ming, granting protection from the Japanese. Using the diplomacy macro builder, send diplomats to improve relations with neighbouring and threatening countries. Send a trader to collect trade in Nippon and save the other until Girin becomes accessible, at which point he should be sent to transfer trade to Nippon. Build light ships up to the naval force limit (and sailor resupply rate) to protect trade in Nippon. The strategy is otherwise the same as with Ternate / Tidore: develop and promote mercantilism. This strategy pairs well with City of Cities.
This way is very easy, very fast, yet does fall on the boarder of what might be considered an exploit. This strategy works for other countries present in two trade nodes, with only one having 3 Centers of Trade under your control
Effectively, what you want to do is move your Trade Capital into the Genoa node, and start collecting with a merchant into the Valencia Trade Node. Then all you want to do is grant the Burgers the "Exclusive Trade Rights" Privilege that gives you 3 mercantilism. After this, recall your merchant from Valencia, which should automatically get rid of the privilege with no penalty to loyalty. After that, all you need to do is send your merchant back into Valencia for a single day, give the Burgers the privilege again, get the extra +3 mercantilism, recall your merchant to get rid of the privilege, and then repeat until 100% Mercantilism.
Without Mare Nostrum
Republics start the game at 25% instead of the regular 10% mercantilism and can get more mercantilism events than monarchies. Increasing the level of mercantilism happens primarily through events, but Genoa has seven unique conquest missions, each granting a 2% boost upon completion, making them a favorable choice for the achievement.
Further ways to raise mercantilism include investing 50 papal influence and taking mercantilism increases from certain decisions. The "Close Foreign Trade" mission available to Chinese tech group nations, for example, adds 5%. The various mercantilism events, along with some Trade idea group events, can also grant several mercantilism increases. Plutocratic ideas also have an event for mercantilism as well as republics. Note that some events may not fire if mercantilism is already 95% or higher.
England is also a good choice to attempt this achievement as countries with a parliament can sometimes get an issue to increase mercantilism. England also starts with 25% mercantilism and can easily gain another 10% through the 'make Calais the staple port' decision. They are also catholic and can easily gain cardinals especially if France is beaten. Additionally the Anglican religion allows the player to spend 100 church power for 1% mercantilism.