Try to set each column separately, e.g.
DECLARE @t TABLE (col1 varchar(22),col2 varchar(22),col3 varchar(22),col4 varchar(22))
insert into @t values ('1','2','0','0')
insert into @t values ('3','4','0','0')
insert into @t values ('5','6','0','0')
SELECT * FROM @t
UPDATE @t SET col3 =
case when col1=1 and col2=2 then 'X' --- and col4= 'R1'
when col1=3 and col2=4 then 'Y'-- and col4= 'R2'
when col1=5 and col2=6 then 'Z' END,
col4= case when col1=1 and col2=2 then 'R1' --- and col4= 'R1'
when col1=3 and col2=4 then 'R2'
when col1=5 and col2=6 then 'R3' END;
SELECT * FROM @t