Nice looking girl!
I take it you have been trimming nails but she makes it difficult? For me, nail clipping isn't an optional activity. You don't like it, too bad, it will happen. That said, Basenjis are very open to bribery. If she is that opposed to the activity I would start with "one nail=one treat". If this makes her more cooperative I would use it but gradually cut back the treats to one per paw, one per two paws, etc.
Most animals don't like being tightly restrained. When things become too stressful it's good if they can walk away for a minute or two before you resume (make sure you have them confined to a room so it doesn't turn into a game of chase), and if they know you are persistent usually things will go fairly easily......unless you have inadvertently taught them that resistance in not futile! (don't make the mistake of letting go if they struggle. Wait until they stop, then reward by releasing)
My girl Tamu hated having her nails done. She would tolerate it for a while, but you could see her expression change. Finally she would have enough of it, and would vocalize "arrr" and grab the offending hand. She never bit down, she knew better than that, but made her objections clear. I would give her a break, (trying not to laugh), then start again. I was showing her at the time so keeping her nails trimmed regularly was essential.
None of my Basenjis has enjoyed this necessary evil, but they seemed to understand that cooperation got it over with quickly. I never needed a muzzle and mostly I did it with the dog upside down on my lap, feet in the air, either head or butt pointed towards me. We must have been quite a sight!