thick-skinned
Immune to or able to ignore the verbal attacks or criticisms of others. You have to be pretty thick-skinned if you want to be in the entertainment industry. For how much she mocks other people, you'd think she'd be a bit more thick-skinned than that.
*thick-skinned
Fig. not easily upset or hurt; insensitive. (The opposite of thin-skinned. Typically: be ~; become ~; grow ~.) Tom won't worry about your insults. He's completely thick-skinned. Jane's so thick-skinned she didn't realize Fred was being rude to her.
thick-skinned
mod. able to withstand much criticism. (Compare this with thin-skinned.) You gotta be more thick-skinned if you want to be a cop.