How do I kill a powerful player without PVP?

Trap design in Minecraft is nearly as complex as it is IRL. It's about presentation, and the mechanism. All traps will require you to prepare the field in advance, and to be able to do so undetected. Given that you're looking to destroy him and his items, I'd recommend being the bait, yourself.

Here's a recent article with some ideas for reference: https://www.sportskeeda.com/minecraft/top-5-minecraft-traps-fool-friends

What Minecraft traps have in common is fairly simple:

1. A Trigger of some sort.
2. A damage-dealing element (TNT is classic, but puffer fish, arrow dispensers, and lava are all viable - as is straight-up fall damage in many cases.)
3. A lure to draw the victim in.

#3 is probably going to be your issue, unless your brother is hunting you the moment you login - in which case gathering enough materials to prepare the trap without getting killed first is the problem. I recommend logging in when he's offline for the preparation phase.

The good news is, you know one thing he loves to do: PvP combat.

Most traps based on a structure will be defeated by the likelihood that he will simply enter the base by making his own door, since destruction of the base is a goal of his. So offer him something else to focus on: a PvP kill that will get away.

A dark cave that already exists on the map is a good venue for a simple "all the TNT" trap. Hollow out the ceiling and fill it with sand and gravel. Place a button or pressure plate trigger connected with redstone to the TNT cluster under the floor (ideally the entrance-end of it, so that the explosion propagates from behind him, towards him, making him more likely to jump directly into it if he hears the fuse.

With a 1-tile-thick destructable ceiling (like dirt which occurs naturally in caves), and a large volume of sand/gravel above it the process goes like this:

1. TNT goes off, hopefully several blocks of it get him in their direct damage radius killing him instantly.
2. If that doesn't kill him, the ceiling above has been destroyed now as well, and he's in a crater beneath it, wounded. Being caught in falling sand/gravel will inflict further damage, and if he's caught in it he'll start drowning.
3. If you used a naturally occurring cave and he survives 1 and 2, he'll be pretty well softened up and hopefully dropped into a natural cave and be picked off by mobs - or you, if you didn't die during the triggering of the trap.

This will be most effective if you're in the trap with him. You will also die, and lose all of your stuff, but that's part of selling the trap.

If you survive and he doesn't, you can either grab his stuff, or get a bucket of lava and simply incinerate everything. But plan to die in your own trap.

Some notes:

If he's truly paranoid about traps, then he'll wear a full set of blast resistant armor and the TNT won't soften him up as much as you'd hope, you'll need thicker sand-fall to finish the job.

If you want to go FULL ACME, and don't mind the mining/smelting necessary.... anvils fall like sand does. Bonus points if you say "Meep! Meep!" in chat after he gets flattened by one.

There's a number of delayed trigger mechanisms you can use to add layers of falling TNT into the mix, five sets of delayed TNT of four blocks of more will absolutely kill anything dead, but the wiring for that is so elaborate you're unlikely to finish before being detected.

If he likes to kill with a Bow, simply place the beginning of your trap a few blocks before a 90-degree corner in the cave. Flee from him around that corner. Now, to get the shot angle he needs to follow you around. Trigger as soon as he comes around the corner and begin attacking him in melee. In all the fuss he may not even hear the TNT fuse.

Trap design is a dense field. Good luck.