First bit of advice playing Demigod, a lot of people seem to have trouble with the Unclean Beast, specifically his spit skill. Here are my thoughts as to how to handle him.
The beast is one tough cookie, especially if he spit spams (they all seem to). Even with a range class you will have to back up a lot and keep him away from you till you are powerful enough to kill him. Here are some things that have helped me (regardless of demigod choice).
--If you really really want to just counter beast there is a favor item that removes the DoT portion of spit, I think its on a 30 second cooldown.
--Combat health pots help, 750 health .5 sec cast time.
--Stay away and dance backward then forward when you see him till he targets something else, only clash with him when you think you will have the upper hand (this is true for all demi’s and matchups really).
--Get wand of speed (1050 gold I think, 25% speed increase for 8 seconds on use, 30 second cooldown or something like that).
Those are a few of the things that help. Sedna (heal), oak (shield), erubus (mist), QoT (sheild), all have built in ways to deal with spit as well.
I used to have a lot of trouble against him, I now feel pretty confident though he is definately tough to beat. Now my main issue is Erebus :-)