What coordinate system do you want this in?
Ok. You were doing the correct procedure at first.
1. Import points into C3D
2. Output tab of the ribbon, Export Civil Objects to SDF
3. Set your projection
4. MAPIMPORT, select SDF file you just created
5. Uncheck everything except for Points. In the Data column click in the cell, then click the ellipsis...
6. Once in there, toggle the radio button for Create Object Data, the select the button for Select Fields...
7. Make sure they are all checked, then click OK.
8. Now you can MAPEXPORT out to a SHP file.
If you want to avoid jumping through hoops, MapWorks Points contains Point Shapefile Read/Write tools that (in the case of export) creates a shapefile directly from the AECC_POINTS in a quick single step.
It is very good, but it doesn't read AECC_POINTS inside Civil3D.
The quickest and easy way I would do it is save the civil3D dwg as an AutoCAD dwg file format. (ExporttoAutoCAD)
Then in that dwg use map export to export to ESRI shp format. When you export open the "Options" tab, click on "Drivers" and check the radio button for 3D.
Simple and no 3rd party or other formats needed other than the dumb down AutoCAD dwg format.
Simple and no 3rd party ...
Also your procedure gives you no point numbers, no descriptions, etc.