The error is very likely logged either to one of the system logs (by way of the syslog daemon), to the kernel log (reviewed using
dmesg), or both.
I would try
dmesg | less first to review the kernel log (you can use
/ to initiate a search).
If that does not turn up anything, turn to the system logs in
/var/log. I'm not sure which exact file this would be on Arch, but something along the lines of
grep -rHi grub /var/log/* | less should get you started.
If neither of these turn up anything useful, with a bit of trickery you may be able to set up a serial console. That is a very different question and quite frankly not likely to be needed, but if you need to, despite its age you may find that the remote serial console howto provides some insights.