[Solved]-Highcharts : Display the labels (min, max, median etc.) in boxplot-Highcharts

Unfortunately this option is not supported, only what you can do is use renderer to add custom text inside chart, but I'm aware that it can be not comfortable solution. http://api.highcharts.com/highcharts#Renderer.text()

Obviosuly you can reqest your suggestion in our user voice system http://highcharts.uservoice.com/

Add another data series, which is a type of "Scatter" and apply the data labels to this series using Marker. The trick is to use the same fill color as your background color and 0 line width so the marker will not be visible and only the label will be shown.

{
        name: 'Outlier',
        color: 'white',
        type: 'scatter',
        data: [ // x, y positions where 0 is the first category
            {
                name: 'This is my label for the box',
                x:0,   //box index.  first one is 0.
                y:975 //it will be bigger than the maximum value of of the box
            }
        ],
        dataLabels : {
            align: 'left',
                enabled : true,
                formatter : function() {
                    return this.point.name;
                },
            y: 10,
            },
        marker: {
            fillColor: 'white',
            lineWidth: 0,
            lineColor: 'white'
        }
    }

Not possible out of the box, but as mentioned by Steve Gu achievable by scatter. You can even ignore the formatter and disable the marker alltogether:

{
  series: [
    {
      type: 'scatter',
      tooltip: {
        enabled: false
      },
      dataLabels: {
        format: '{key}',
        enabled: true,
        y: 0,
      },
      data: [{ x: 0, y: 975, name: '975'}],
      marker: {
        enabled: false,
      }
    }
  ]
}

just disable marker and set format to key.