One way to do it is to use sec_axis(). Here I have created two data frames. Both y-axis (RT1 and RT2) are on the same scale. Target1 and Target2 are on different scales.
df1 <- data.frame(Target1 = c(1,2,3), RT1 = c(1,2,3))
df2 <- data.frame(Target2 = c(20,30,40), RT2 = c(3,4,5))
To demonstrate the effect, I'm using scatter plot for df1 and line plot for df2. I also divide Target2 by 10 to bring the x variables closer and easier to be compared.
ggplot() +
geom_point(data = df1, mapping = aes(Target1, RT1)) +
geom_line(data = df2, mapping = aes(Target2/10, RT2)) +
scale_x_continuous("Target 1", sec.axis = sec_axis(~.*10, name = "Target 2"))

or, if you don't want to rescsale the x-axis, you can use dup_axis() instead.
ggplot() +
geom_point(data = df1, mapping = aes(Target1, RT1)) +
geom_line(data = df2, mapping = aes(Target2, RT2)) +
scale_x_continuous("Target 1", sec.axis = dup_axis(name = "Target 2"))

Hope it helps.