To think I can rescue this cactus?

[WallToWallBastards]

I love a good low effort plant and at Christmas I bought 2 cacti, a succulent and an air plant. The air plant lasted 2 weeks. The succulent looks like it's on its way out but I remain hopeful. My friend thinks I should be publicly shamed for my crimes against plants but I'm sure I can do something magic or sciencey.

Hope is renewed. I live in a city centre so I'm scratching my head for a B&Q, never seen cactus compost even in the fancy hipster places wot do sell fancy cacti. There's a skip outside my house with a bag of ominous sandy looking stuff so I might borrow some of that instead.
Now what do I do with the tiny green shooty bit that looks like an arm reaching for help? my aunty shamelessly takes clippings of every plant she likes the look of but I don't know what she does with them.
Now to see if you can help me with my sad succulent

Succulent was fine until a few days ago. Also photographic evidence that I have the Ray Mears of cacti here.