As Agony said, it's a technique called Mode 7. Basically it's a normal 2D tilemap which can be scaled in both directions. To create the Mode 7 fake 3D effect, the scaling parameters and offsets are adjusted per scanline.
If you search for Gameboy Advance development tutorials you should come up with a complete description on how to do this sort of thing.

I still don't understand what '3d look' you're trying to avoid while still making a 3d-style game. Sure, it will 'look' 3D because of the high quality scaling, rotation, and texture filtering that we have on hardware these days... you want to take that away?

I think pixelation is the #1 thing that defines the "look" that you want. Use D3D and nearest neighbor texture sampling if you insist on feeding your nostalgia!