As per the title, the Survivor achievement says to survive combat with low health 250 times.
But how low is low?
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It's below 5% of your maximum health.
I had a bug where the achievement was incorrectly awarded to me the first time where I survived a fight with low health (I just realized this now since you're asking about it, it seems like it wasn't added to the achievements list, though).
It said something like "Have under 5% health in a fight and survive".
It's <10%. This one can be cheesed fairly easily, as the achievement is tested whenever you change zones. Just round up a melee mob or two and train them to either a waypoint or a zone exit and let them hit you until you just below 10%, then leave the zone. Remove all +HP/sec gear and your weapon, zone back in and punch the mob then quickly zone back out, and you should get the notification. Usualy it takes at least a second or two for the mob to realise you're there and attack you, so you should be able to zone in and out without being touched :)
Repeat 250 times and you're done. It's boring as hell, but 'only' took me about 10 minutes with a level 45 character in Nightmare ActIII using the Bastion's Keep Stronghold <-> Skycrown Battlements portal and a pet Fallen Mongrel.