You have to do a bit of extra work to start X in virtualbox with archlinux. You can find it on the wiki here, copied and pasted below.
Installing Arch under VirtualBox is straightforward, and additions should be installed through pacman (not through "Install Guest Additions" in VirtualBox, or a mounted ISO.) Follow these instructions after doing a basic install of the X-window system found on the Beginners' Guide.
Guest additions package
Manually load the VirtualBox modules with
# modprobe -a vboxguest vboxsf vboxvideo
To autostart these modules each time you boot, you can add the three modules above to the MODULES array in /etc/rc.conf.
MODULES=(... vboxguest vboxsf vboxvideo)
The VBoxClient contain these services(/usr/bin/VBoxClient-all) (copy/paste...) :
--clipboard start the shared clipboard service
--display start the display management service
--checkhostversion start the host version notifier service
--seamless start the seamless windows service
So you can Enable VBoxClient-all to start all these services.
If you are running something that launches /etc/xdg/autostart/vboxclient.desktop, such as GNOME, then you should be ready to go. If you use .xinitrc to launch things instead, you must add
to your .xinitrc before launching your WM. You should now be all set, and all guest additions should work properly.