Look at the attached movie.

I set

        x_axis.setTickLabelRotation(45);
        y_axis.setTickLabelRotation(45);

But you can see, that I changed height of scene, and y_axis labels rotation changed from 45 degrees to 90 degrees.

Code is here :

    @Override
    public void start(Stage stage) {
        VBox content = new VBox();
        Series s1 = new Series( FXCollections.observableArrayList(
                    new XYChart.Data("First", "Green"),
                    new XYChart.Data("Second", "Blue"),
                    new XYChart.Data("Fourth", "Red")
                ));
        s1.setName("Set 1");
        Series s2 = new Series( FXCollections.observableArrayList(
                    new XYChart.Data("First", "Red"),
                    new XYChart.Data("Second", "Green"),
                    new XYChart.Data("Fourth", "Blue")
                ));
        s2.setName("Set 2");
        Series s3 = new Series( FXCollections.observableArrayList(
                    new XYChart.Data("First", "Blue"),
                    new XYChart.Data("Second", "Red"),
                    new XYChart.Data("Third", "Green")
                ));
        s3.setName("Set 3");
        ObservableList data = FXCollections.observableArrayList(s1, s2, s3);
        Axis y_axis = new CategoryAxis();
        Axis x_axis = new CategoryAxis(FXCollections.<String>observableArrayList("First", "Second", "Third", "Fourth"));
        Chart chart = new ScatterChart(x_axis, y_axis, data);
        content.getChildren().add(chart);
        stage.setScene(new Scene(content, 400, 400));
        stage.show();
        x_axis.setTickLabelRotation(45);
        y_axis.setTickLabelRotation(45);
    }