IPA: /ˌʌn.rɪˈlɛn.tɪŋ.li/
KK: /ʌnˈrɪlɛntɪŋli/
In a way that does not give up or stop; showing no mercy or flexibility.
She pursued her goals unrelentingly, never allowing obstacles to deter her.
Unrelentingly → It is formed from "un-" (meaning not), "relent" (from Latin "relentare", meaning to soften or become less severe), and "-ingly" (a suffix used to form adverbs). The word means to do something in a manner that does not soften or lessen in intensity.
Think of 'not softening' ('un-') and 'becoming less severe' ('relent') to remember that 'unrelentingly' means doing something with unwavering intensity.