Accepted answer

I think that you just need to set type of Y axis as:

yAxis: {
    type: 'datetime'

...and write other code like if X axis has type 'datetime' but keep in mind that axes were swapped. Also don't forget that you need to customize your tooltip to format the datetime value (use the property tooltip: formatter). Also as I see in your picture you need to customize datetime labels of your Y axis. You may use the property labels: formatter for X axis.

So there is an example:

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