Here is my attempt at it:
# I re-added the old column titles
prism_data <- read.table(text="
Cell-Line   Aneuploidy.Aneuploidy.score   Aneuploidy.Ploidy
ACH-000001  26  3.52    
ACH-000007  8   2.28    
ACH-000008  22  2.63    
ACH-000012  21  2.74    
ACH-000013  21  3.13    
ACH-000014  8   3.07", header=TRUE)
library(tidyverse)
prism_data %>% 
  mutate(Cell_num = as.numeric(str_extract(`Cell.Line`, "\\d+"))) %>% # you could probably get the same effect by converting the cell line column into a factor column, but I chose this way instead (getting the number part of the cell line string)
  ggplot(aes(x = Cell_num)) + 
  geom_line(aes(y = Aneuploidy.Aneuploidy.score), colour = "blue") + 
  geom_point(aes(y = Aneuploidy.Aneuploidy.score), shape = 17, size = 3, colour = "blue") + 
  geom_line(aes(y = Aneuploidy.Ploidy * 10), colour = "red") + # the ploidy data needs to be scaled up, so that it is roughly of the same magnitude as the score data
  geom_point(aes(y = Aneuploidy.Ploidy * 10), shape = 15, size = 3, colour = "red") +
  scale_y_continuous(sec.axis = sec_axis(~./10, name = "Aneuploidy.Ploidy")) +  # adding a second column
  theme_bw()
 I wasn't able to get the x axis names the same (are they the names of cell lines?)
I wasn't able to get the x axis names the same (are they the names of cell lines?)