How to remove the handles from this joint bathroom faucet
Tough to tell exactly from the pic but it appears the only way to access the cartridge/washers inside would be to close both water supply lines, and carefully unscrew the flange (round top piece) that mounts to the valve body with a pair of pliers using caution not to scratch the chrome finish. Once that flange in removed the entire faucet handle and guts should screw out.