HighCharts turn animation false for line chart

It's the same that I answered here but you have to change column to line.

plotOptions: {
    line: {
        animation: false
    }
}

demo

If you want to remove animation from all types you can use series instead.

plotOptions: {
    series: {
        animation: false
    }
}

If you want to completely disable all animations in Highcharts (also these happening when toggling lines on or off) use the following:

chart: {
    animation: false
}

See http://api.highcharts.com/highcharts#chart.animation for more information. (demo)