on one's last legs大体上有两个含义：

1. 非常疲倦

He has worked all day and looks like he's on his last legs.

他工作了一整天，看起来很疲倦。

We'd been out walking all day and I was on my last legs when we reached the hotel.

我们走了一整天，回到旅馆时我累坏了。

2. 病危，奄奄一息，行将就木,频临死亡；处于崩溃或死亡的边缘，快完蛋了，快报废了，快倒闭了；大势已去；玩儿完；没戏

The doctor says she's on her last legs.

医生说她病情非常危急。

You' ll be on your last legs if you keep worrying this way.

你再这样担心下去，会崩溃的。

My old car is on its last legs.

我的旧车快挂了。

The fridge has been used for twenty years and is now on its last legs.

这座桥已经使用了二十年了，现在快报废了。

Like a grasshopper at the end of autumn, the enemy is on his last legs.

敌人像秋后的蚂蚱，蹦跶不了几天啦。

This relationship is on its last legs.

这段关系已经快玩儿完了。《柯林斯高阶英汉双解学习词典》

Dick's firm is on its last legs.

迪克的公司就要倒闭了。

另外.旅行的最后一站

The Prince will visit Boston on the last leg of his American tour.

亲王美国之行的最后一站是波士顿。《牛津高阶英汉双解词典》

The first leg of the journey was by boat to Lake Naivasha in Kenya.

行程的首段是乘船到肯尼亚的奈瓦沙湖。

注意：这里的leg用了单数。