I can think of two ugly hacks that work ...
The first is to set the default font size of all text labels for the plot
h = figure;
set(h, 'DefaultTextFontSize', 30);
The second is to change the text label after plotting
h = boxplot(MPG, Origin);
set(findobj(get(h(1), 'parent'), 'type', 'text'), 'fontsize', 30);
It is not clear to me what boxplot is actually returning. It is an array of handles, when I would have expect the group. My guess is if you look through the code of boxplot you can find a cleaner way.
If you only have the figure file
hFig = figure;
You can open the figure and get the handle to the figure
hFig = open('temp_figure.fig');
The goal is then to find the boxplot object. Unfortunately, the boxplot object this is just an hggroup object and there might be lots of hggroup objects which are not boxplot objects. I don't know how to figure out if an hggroup object is actually a boxplot object. You can however, click around and select objects until gco works:
set(findobj(get(gco, 'Children'), 'type', 'text'), 'fontsize', 30);