I got him at 10:38am Australian Eastern Standard Time. (AEST)
the spawn timer on him is believed to be 6-8 hours, and others say 10-12 and even 24 hours..
i was farming him since 3pm Tuesday afternoon AEST but there was a server shutdown at about 7pm that day for 8 hours. i set my alarm for 4am to get Arcturis straight away but over slept an hour, so i roughly calculated that he would of been tamed or killed at 4-4:30am AEST which means he has a 6 hour respawn! so GOODLUCK! hope this helps!