Add another layer of scatter plot on top of box plot like below to show like the image above.
For Example -
ggplot(mpg,aes(drv,displ))+geom_boxplot()

ggplot(mpg,aes(drv,displ))+geom_boxplot() + geom_point()

To add color to data points, add col = "color name" inside geom_point()