With the following data:
Method Metric E0 E1 E2 E4
Method-XXX Precision 0.9661017 0.9622642 1 0.9655172
Method-YYY Precision 0.533 0.535
Here's a way to get all the labels without rotating. You plot the axis labels on two lines instead of one to avoid overlap. I've done it with a single graph to demonstrate the method.
dat <- read.table("http://dpaste.com/1563769/plain/",header=TRUE)
# Create barplot
barplot(height=dat$E0, beside=TRUE, col=c("red","blue"))
# Get x-coordinates of bars
x.coords = barplot(height=dat$E0, beside=TRUE, plot=FALSE)
# Create new coordinates between each pair of bars
new.x.coords = seq(sum(x.coords)[1:2]/2, sum(x.coords)[9:10]/2, x.coords[2]-x.coords[1])
# Plot axis labels, but not axis or tickmarks
axis(side=1, at=new.x.coords[c(1,3,5)], labels=dat$Method[c(1,3,5)], line=0, tick=FALSE)
axis(side=1, at=new.x.coords[c(2,4)], labels=dat$Method[c(2,4)], line=1, tick=FALSE)
# Plot just axis and tickmarks, but not labels
axis(side=1, at=new.x.coords, labels=NA)