Not sure if this helps, but you might look at something like:
install.packages("palmerpenguins")
library(palmerpenguins)
boxplot(body_mass_g~sex+species, data=penguins, frame=F, col = c("#00AFBB", "#E7B800"), names=c("Adelie.F", "Adelie.M", "Chnstrp.F", "Chnstrp.M", "Gentoo.F", "Gentoo.M"))
I think the format of your data frame would need to change to something like:
Month | Reading | Value
Jan TmaxRCP2.6 ...
Jan TmaxRCP2.6 ...
Jan TmaxRCP2.6 ...
Jan TmaxRCP8.5 ...
Jan TmaxRCP8.5 ...
Jan TmaxRCP8.5 ...
or similar