There's two elements to elevating privileges - one is specifying the user to run as, the second is authenticating. In most cases the authentication element is going to prompt the user for a password.
If you know the admin password you can embed it in your script, but if this is going to run on a remote user's system then you'll need the prompt.
In addition, if this is running on other systems you cannot write it using hard-coded paths - what English systems know as 'Application Support' may be something completely different in other languages. Therefore you'll need to use specific AppleScript commands to find the files.
set file1 to POSIX path of (path to application support as text) & "Foo" -- /Library/Application Support/Foo
set file2 to POSIX path of (path to preferences from local domain as text) & "Foo" -- /Library/Preferences/Foo
set file3 to POSIX path of (path to library folder as text) & "Receipts/Foo" -- /Library/Receipts/Foo
set file4 to POSIX path of (path to applications folder as text) & "Foo" -- /Applications/Foo
set file5 to POSIX path of (path to preferences from user domain as text) & "Foo" -- /Users/username/Library/Preferences/Foo
do shell script "rm -rf " & quoted form of file1 & space & quoted form of file2 & space & quoted form of file3 & space & quoted form of file4 & space & quoted form of file5 with admistrative privileges
If you can/want to embed the password, just append 'password "blah" to the 'do shell script' command.