Cities: Skylines

In order to build the Hadron Collider Monument you must first unlock the ability to build monuments, which is achieved when your city population reaches 90,000. You will also receive this achievement when they become available:

Once you have unlocked the ability to build monuments, the Hadron Collider requires six unique bulidings to be built in your city that each have their own objective to unlock them. The unique buildings and their requirements are as followed:

The total price to build all of these unique bulidings and monument is 1.21million, excluding required objectives which may vary depending on your city.

Statue of Shopping
Cost to build: 10,000
Requirement to unlock: City money must reach -1.
Basically go into debt

Posh Mall
Cost to build: 45,000
Requirement to unlock: All tax rates must be no greater than 4% for 20 consecutive weeks.
Tax rates can be changed by holding and selecting Economy, then choosing the Taxes tab to change the tax rate for each building type. NOTE: some policies, if enforced, may alter the tax rate after the fact so be careful.

Colossal Order Offices
Cost to build: 70,000
Requirement to unlock: Weekly education expenses at least 20,000 for 10 weeks.
Building schools and universities will increase your education expenses. There is also an Education Boost policy under Services on the City Policies page that will increase your education budget by 25%.

Grand Library
Cost to build: 90,000
Requirement to unlock: Construct 7 universities and maintain them for 10 weeks.
Simply build 7 universities in your city and keep them running for 10 weeks.

Aquarium
Cost to build: 20,000
Requirement to unlock: 5,000 children in elementary schools.
You can check your education stats by holding in game and selecting Info Views. From here, select Education on the left side (icon of an open book), and tab to Elementary. From here, you can see how many children are elegible (if too low then build more houses) and how many your already bult schools can facilitate (if lower than 5,000 build more elementary schools).

Theatre of Wonders
Cost to build: 175,000
Requirement to unlock: Construct 3 Elementary Schools, 3 High Schools and 3 Universities.
Should be pretty simple to do. Just build whatever you need to match these numbers.

After you have unlocked and built all 6 of these unique buildings, the Hadron Collider Monument will become available for you to build for another 800,000. Once you have placed this in your city the achievement should unlock!