Reversing direction of an AC universal motor
The link that you provide and the comment by John D say what must be done. The armature and field connections must be reversed with respect to each other. In the diagram, you disconnect the black lead and the red lead from the two brushes and reconnect each to the opposite brush.

The two red wires going to the field assembly are two wires, not one continuous wire. One end of the field winding is connected to each red wire.

Here is a marked version of the diagram. You could swap the field connections instead of the brush connections if that is easier.



Caution

If there is a nut holding the blade onto the motor shaft, reversing the motor will tend to cause the nut to loosen when the motor is operated in reverse.