PL/SQL Developer: Multiple statements?
I think you're using the Test window. This can only execute a single statement. The SQL Window and the Command Window are able to run multiple statements.
If you need to run this in a Test window, you can embed it in a begin..end block to make it a PL/SQL statement block.
I also faced this error. You need to go to tools->preferences. In window types go to SQL window and select "Auto select statement". This should remove the error.
try this way;
UPDATE TableX SET Field1 = 'New value 1' WHERE Field2='1'/UPDATE TableX SET Field1 = 'New value 2' WHERE Field2='2'/UPDATE TableX SET Field1 = 'New value 3' WHERE Field2='3'/