What is a word for someone whose emotions are not hurt easily? I'm looking for something more specific than 'robust' and 'stable'.
Insensitive could work, but unfortunately it has two separate meanings, so could cause confusion if it's not clear which one is meant:
not feeling or showing sympathy for other people's feelings, or refusing to give importance to something
not showing any reaction to something, or unable to feel something
A better word might be thick-skinned:
Someone who is thick-skinned does not appear to be easily hurt by criticism
Or if it doesn't have to be a single word, you could try a phrase like "immune to criticism" or "hard to offend".