I'm currently trying to present my data but I'm having some trouble deciding what graph to use...

I'm studying the effect of alcohol concentration on gene expression.

I have two categorical variables. One is the alcohol concentration (0, 1 and 2 %) and for the other I've graded gene expression in my samples from 1 - 4. For each concentration i have three groups and in each group i have around 4 samples.

I was thinking on doing a boxplot but I'm not sure if i have to have continuous data on one of the axis?

I still don't completely understand the data you have. What do you mean with " For each concentration i have three groups" is this referring to the graded gene expressions?

For Boxplots indeed you should have numerical (continuous), if your grading indeed can be understood as expression 4 is roughly 2 times that of expression 2 and 4 times that of 1 it could be used.
I would probably go for a stacked bar-plot to show the proportions of each of the groups.