Wyll the warlock may not be our favorite Baldur's Gate 3 companion, but that's only because the overall standard is so high. In any other RPG he'd be a top pick, and even in Baldur's Gate 3 he's worth keeping around. It's just a shame you can't complete his personal quest, which earns you a sweet Infernal Robe and prevents him from growing a pair of horns, without killing Karlach, who is everyone's number one fave.
Except you sort of can. The sequence of steps necessary to thread this particular needle has been figured out by various folks, including Leyllara on the BG3 subreddit. Here's how it works. First, you recruit Wyll and get the quest to kill Karlach on behalf of his fiendish patron, Mizora. Then you leave Wyll at camp and kill Karlach without her realizing you're the one who did it. This is tricky, but can be done by attacking from range, or casting a hold person spell. What you want is for the barbarian to drop before her dialogue triggers. You can also disguise yourself before attacking, which may be tough at low level unless you've got the Mask of the Shapeshifter from the digital deluxe DLC.
