Band of Brothers

Alright gonna try to share my experience with this achievement:

Important! For this achievement you not only have to be in a group (or raid), your party members also have to have Warmode turned on and be in the same zone as you, and maybe even within range of you

- Honorable Kill
This part is pretty easy and self explanatory

- Loot Player Bounty
After killing 10 players from the opposing faction while in Warmode in Kul Tiras/Zandalar players will become "Assassins" and gain the buff Alliance Assassin or Horde Assassin. After a while and a few more honorable kills, the Assassin will gain the debuff Bounty Hunted which will make them appear on the opposing factions map and drop a Player Bounty when killed. You just have to be in a 2-5 man group (raid should work as well), kill an Assassin with the debuff and loot the bounty. Bear in mind that only 5 players can loot a bounty before it disappears.

- Complete Rare Elite World Quest
Easy and self explanatory

- Loot War Supply Chest
This was the toughest part for me. The War Supply Chests will appear after a player has opened the War Supply Crate. The crates are dropped from the sky by an airplane every 10-20 minute in every zone in Kul Tiras/Zandalar. They will only appear for you if you have Warmode on. It's a 8 seconds cast to open the crate, and if an alliance player opens it, only alliance players will be able to loot the War Supply Chest inside and vice versa. The supply chest is instantly looted, and will disappear 45 seconds - 1 minute after the War Supply Crate is looted.
I found the best spot for doing this, is going to the mountains just south of Vulpera Hideaway, turn up view distance to max and wait (alternative spot is atop Dazar'alor). You will be able to see the airplane in the horizon and you will be able to hear it. It will drop the crate, and while the crate is falling to the ground it will be targetable. The way I did it, was wait at the mountain, and when I saw the airplane I waited till it dropped the crate, then Goblin Glided down and looted it. While it was falling I used the macro
/tar War s
/run SetRaidTarget("target",8)
To track it with skull marker.
After the crate has landed it will be untargetable.

Good luck with the hunting!

i looted a war supply cache while in a group of 2 but i get only war supplied achievement and not -loot war supply chest part of this achievement, maybe cos the player of the party was in another zone?

This is obtainable in the pre-patch. A "Rare Elite World Quest" can be done with the "DANGER" type world quest.