In your X-COM Apocalypse folder, there will be a folder named "Ufodata".
Open up this folder and scroll down until you see a series of files named "Citymap#" and "Citymap#.bld".
Citymap1 is Rookie
Citymap2 is Easy
Citymap3 is Normal
Citymap4 is Hard
Citymap5 is Superhuman
The next step is easy;
Take the original difficulty map file (say, Citymap3 and Citymap3.bld) and rename them to something else (like CitymapNormal & CitymapNormal.bld) and then rename the version you want to take it's place (say, Citymap 5 and Citymap5.bld) to their name.
So in this case;
Citymap3 becomes CitymapNormal
Citymap3.bld becomes CitymapNormal.bld
Citymap5 becomes Citymap3
Citymap5.bld becomes Citymap3.bld
Et voila, you should now be presented with the Superhuman map when you try to play Normal mode.
Take in mind that Apocalypse will probably crash if you try to run Superhuman after that, because it'll have no corresponding map files unless you renamed the original Citymap3 to Citymap5 after replacing it.
It is also important to rename the corresponding .bld file, as I believe this tells the game which buildings belong to who, and so on and so forth.
Note that this will not change the difficulty level - just the map you play on. The game should work fine after this assuming you did it right, and it's nice for a change of scenery.
If you're feeling adventurous you can also edit the maps using XME although this isn't adviseable and may cause errors. EDIT by j'ordos: XME cannot save changes. There is an option for it in the program but it doesn't work! Best to know that before wasting hours on a new map.
Edited by j'ordos, 06 November 2009 - 07:17 AM.