After looking for an alternative for FOR EACH in SQL Server, I found that a CURSOR can be used. It serves the purpose, but need somebody to validate this.
CREATE TRIGGER Trg_Institution_FieldAudit_1 ON dbo.Institution FOR UPDATE as
-- DECLARE Variables
DECLARE institution_cursor CURSOR DYNAMIC FOR SELECT * FROM DELETED
OPEN institution_cursor FETCH NEXT FROM institution_cursor INTO -- @variables here
WHILE (@@FETCH_STATUS = 0)
BEGIN
IF UPDATE(COL1)
BEGIN
INSERT INTO AuditTable VALUES (COL1, @prev, @next);
END;
FETCH NEXT FROM institution_cursor INTO -- @Variables here
END
CLOSE institution_cursor
DEALLOCATE institution_cursor