But the real backbreaking is that carried out by farmers who use irrigation.
我大概知道它的意思是但是真正累人的是那些使用灌溉的农民，但是carried out什么意思呢

又一个没有看清楚原文的例子。原句出自 "The Economist" 2003年12月18日的一篇文章 "Climate change and civilisation - Time and chance"：
But the real back-breaking, health-destroying labour is that carried out by farmers who use irrigation.
"carried out" 是“进行”的意思。
大意是那些灌溉庄稼的农夫所做的工作才是真正的劳累和有害健康。