The Governments requirements for 'The Great Wall of Trump' (I called it that, not the government) The article does link to documents, but you have to download them, I'll list the stuff mentioned in the article though.
-Wall must be 'physically imposing', between 30 and 18 feet, ideally 30, higher if you can.
-"The wall must also be impossible to climb without a ladder, and should make it difficult to use "common and more sophisticated climbing aids," like grappling hooks. "
-In addition, the wall must resist attempts to penetrate through or under it. The request specifically mentions it must successfully endure for at least 30 minutes -- but ideally more than four hours -- attempts to bore through it with a "sledgehammer, car jack, pick axe, chisel, battery operated impact tools, battery operated cutting tools, Oxy/acetylene torch or other similar hand-held tools."
-It must be aesthetically pleasing with a nice color (a BEYOOUTIFUL Wall)
-It must blend in with the landscape or match it's surroundings.
-After initially saying the wall should be made of concrete, the government widened its call and said it would consider "other designs." On Friday, it suggested non-concrete designs "may not be entirely solid" and could feature "a see-through component" so the border patrol would have "situational awareness" of the Mexican side.
So, it's quite a tall (pun intended) order and an engineering challenge, that's for sure. Also, 'tall and imposing' and 'blend with the landscape' don't really go together iMO for a manmade structure since it seems like you'd want it to be obvious because imposing means it would stand out. Unless we're talking about natural stone or something.
edit: I just realized that there's nothing regarding ecological considerations, which would throw an entire bag of new wrenches into the mix.
edit2: Maybe they could have added 'as cheaply as possible' because it'd be in the governments interest to have it be as cheap as they can get it.
Edit3: Oh, and, they're going to have to adapt to multiple different environments. The border crosses a desert with shifting sand dunes, how you build a wall there is going to be MUCH different than say, in a mountainous area.