The origin of the Aztecs is uncertain,but we know they were located on an island the they build in the capital of Tenochtitlan. They had to build the land on their own by hand. They used rods and filled them in with mud and dry reeds.
One or their achievements were their floating gardens. They had to build their own garden on the water in order to eat. This all happened because the Aztec got whatever was left for grabs in the Valley of Mexico. I think that this is important because without this they wouldn't have enough food to support their civilization.
I think another great achievement would have be their principal temple (main temple). They had to make this large temple by hand and it had to of took more then a few days. This large temple could hold a lot of people at one time.
The game of soccer was created in their time. This soccer is not the kind that we know today. This kind is more deadly and harsh. You had to throw a ball through ring and if you lost you would have to get you head chopped off.
Aqueducts were used to make water accessible from everywhere around their city. Aqueducts are basically a way of getting water over valleys of gaps. This means that this was one of the things that helped them stay alive as long as they did.
The jaguar warriors were members of the Aztec military, they were also the elite military unit. They would go and capture, not kill, but capture prisoners to later be sacrifices to the Aztec gods. To become one you had to capture twelve enemies during two consecutive battles. These people used a weapon called machauhhuil in battle. This was used to hurt the person so they could sacrifices them later.