1. Select the column you want to sort. Then click on "Sort Smallest to Largest".

2. Choose "Continue with the current selection".

You can see, only one column was sorted.

Repeat this for the rest 349 columns :)
In order to do it alltogether in one go:
Open the sheet you want to sort.
Open VBA editor using Alt+F11
Insert > Module
Paste this code:
Sub sort_columns_separately_AZ()
Dim rngStart As Range
Dim rngHeaders As Range
Dim c As Range
Set rngStart = ActiveSheet.Range("A2")
Set rngHeaders = ActiveSheet.Range(rngStart, rngStart.End(xlToRight))
For Each c In rngHeaders
ActiveSheet.Sort.SortFields.Clear
ActiveSheet.Sort.SortFields.Add Key:=c, _
SortOn:=xlSortOnValues, Order:=xlAscending, DataOption:=xlSortNormal
With ActiveSheet.Sort
.SetRange ActiveSheet.Range(c, c.End(xlDown))
.Header = xlYes
.MatchCase = False
.Orientation = xlTopToBottom
.SortMethod = xlPinYin
.Apply
End With
Next
End Sub
- In the code, change
ActiveSheet.Range("A2")
with the cell address where your data table starts, for example ActiveSheet.Range("B5")
.
- Hit F5
Results:

Note: if you have any empty cells in your data, this code will need adjustments in order to work correctly on those columns which have empty cells.