Situation & data
I have a dataframe df of athlete positions in a race (I\'ve already melted it for use with ggpl         
        
Another option using the forcats package.
ggplot(df, aes(x = distanceRemaining, y = forcats::fct_rev(factor(position))))
This has the advantage of keeping everything in the ggplot call, and playing nicely with other options such as coord_flip and facets_wrap(..., scales = "free")
For a discrete axis, using reorder() worked for me. In context of the above problem, it would look something like this:
ggplot(df, aes(x = distanceRemaining, y = reorder(position, desc(position))))
Hope this helps.
Try the following:
g <- ggplot(df, aes(x=distanceRemaining, y =position, colour=athlete, group = athlete))
g <- g + geom_point()
g <- g + geom_line(size=1.15)
g <- g +  scale_y_continuous(trans = "reverse", breaks = unique(df$position))
g

There is a new solution, scale_*_discrete(limits=rev), example:
tibble(x=1:26,y=letters) %>% 
  ggplot(aes(x,y)) +
    geom_point() +
    scale_y_discrete(limits=rev)
                                                                        You just need to turn the position variable into a factor and then reverse its levels:
require(dplyr)
df <- df %>% mutate(position = factor(position), 
                    position = factor(position, levels = rev(levels(position)))
And then with your code you'd get:

as per https://gist.github.com/jennybc/6f3fa527b915b920fdd5:
add scale_y_discrete(limits = rev(levels(theFactor)))
to your ggplot command.