First, please note that SQL Server doesn't support UTF-8, it supports UTF-16. So it's possible that you still have an encoding problem in your application code (you didn't show any sample data or code, so it's hard to say exactly what's going on).
Having said that, you can't simply UPDATE
the data to change it to Unicode:
declare @t table (c nchar(1))
insert into @t select '말'
insert into @t select N'말'
select c, ascii(c), unicode(c) from @t
update @t set c = cast(c as nchar(1))
select c, ascii(c), unicode(c) from @t
As you can see, the character 말 is stored as ASCII 63 if you don't use the N
prefix, and even if you convert it to Unicode explicitly, SQL Server has no way to magically know that you really meant it to be Unicode code point 47568. So the only thing you can do is go back and re-INSERT
all your data correctly.