How to open a shell script in a new Terminal window and run it with administrator privileges
I'd try writing a simple script:

#!/bin/bash
sudo /usr/bin/id


save this as something.command, change its permissions to executable with chmod +x, and then run this from AppleScript with

osascript -e 'do shell script "open -a Terminal ./something.command"'


Instead of /usr/bin/id you can call whatever script you need to run with admin privileges then.

EDIT:

This will work:

osascript -e 'do shell script "sudo /Applications/Utilities/Terminal.app/Contents/MacOS/Terminal" with administrator privileges'