ElementStacks

HTML

<script src="http://code.highcharts.com/highcharts.js"></script>
<div id="container" style="height: 400px"></div>

<button id="toggler">Toggle data labels</button>
<button id="linea">Toggle linea</button>

JavaScript

var chart = new Highcharts.Chart({
    chart: {
        renderTo: 'container',
        defaultSeriesType: 'line'
    },
    xAxis: {
    },
    yAxis: {
    },
    legend: {
        layout: 'vertical',
        backgroundColor: '#FFFFFF',
        style: {
            left: '100px',
            top: '70px',
            bottom: 'auto'
        }
    },
    tooltip: {
        formatter: function() {
            return '<b>'+ this.series.name +'</b><br/>'+
                this.x +': '+ this.y;
        }
    },
    plotOptions: {
        series: {
            dataLabels: {
                enabled: true,
                formatter: function(){
                    return ( this.series.hideDataLabels ) ? '' : this.y;
                }
            }
        }
    },
    series: [{
    id:'0',
        data: [ 71.5, 106.4, 129.2, 144.0, 176.0, 135.6, 148.5, 216.4, 194.1, 95.6, 54.4]        
    },{
    id: '1',
    data: [29.9,106.4, 129.2, 71.5,   148.5, 216.4,29.9, 194.1, 95.6, 144.0, 176.0, 135.6,54.4]
    }]
}, function(chart){
    chart.series[0].hideDataLabels = false;
    
    // Add toggler action
    $('#toggler').click(function() {
    	let id = $("#")
      for(let i= 0;i< series.length; i++){
          chart.series[0].hideDataLabels = !chart.series[0].hideDataLabels;
          chart.series[0].hide();
          chart.series[0].show();
      }
    });
        $('#linea').click(function() {
      for(let i= 0;i< series.length; i++){
          chart.series[1].hideDataLabels = !chart.series[1].hideDataLabels;
          chart.series[1].hide();
          chart.series[1].show();
      }
    });

});