tell application "Screen Sharing"
    activate
    tell application "Screen Sharing"
        activate

        tell application "System Events"
            keystroke "osx-mini.local" -- "osx.mini.local" would need to be replaced by "YourComputerName or IP Address"
            keystroke return
        end tell

    end tell

    delay 2

    tell application "System Events"
        set value of attribute "AXFullScreen" of window 1 of process "Screen Sharing" to true

    end tell
end tell