I have a data-set which consists of 1 continuous (although it can be discrete if I choose to round up the values) dependent variable Y and several categorical and discrete data columns that may or may not have an effect on Y.

Y, in this case, is not normally distributed so to check if a given categorical data-column/independent variable has a significant effect on Y a Kruskal-Wallis test can be used.

However, my objective is to find out which categorical data-column is the most important one, that is has the most significant effect on Y.

Could someone please point me in the right direction, which statistical test/analysis is applicable here?