Can't get faucet cover off

You need to unscrew the 3 elements in red circles. The 2 black plastic retainers, the middle metal nut, which also restrains it, and the water hoses can be removed once the faucet is able to move upward. Remember to cut the water before it reaches the faucet! Happy plumbing!

I ran into the same sort of situation when trying to fix a faucet at the house my son bought. The final answer I found was that the faucet was old and so much corrosion had accumulated on the lever that it effectively welded the two parts together that were supposed to just slide apart. I ended up basically destroying the handle trying to get it off.

It sounds like that 's where you are; the only thing that's going to get those handles off is overwhelming force, which is almost certainly going to damage the finish on either the faucet or the handle. If it was me, I'd be planning on a replacement now.

You could try to take the faucet out of the sink, turn it upside down, fill the space at the bottom of the handle with penetrating oil (something like PB Blaster maybe) and let it soak; that might dissolve enough of the corrosion to let the parts separate.

@g3548dm I don't think you get to the packing and valve stem from the bottom. When you move the handle does the part that covers the stem move as well? I would suggest to pry it up instead of turning it. Double check to make sure there is no setscrew on the side somewhere.

If you are trying to replace a washer, first open the faucet, then remove the handle, then continue turning the inside till it screws out.

If it does not screw out, it is probably corroded stuck.