Requirements: Gauss Weapons and Predator Armor

The first scan will give you four unique weapon. Their stats are better than starting weapons and can be upgraded in the shop after you have done the appropriate research.
Those 4 weapons are MADE to beat those ruler bosses.
Gauss/Plasma research for the pistol and the bowcaster upgrade
Stun Lancer and Archon for the Axe upgrade

5 more things to remember:
THE FROST GRENADE IS SUPER USEFUL
Mimic beacon and Flashbang does not work on those bosses.
Before attacking try to shred their armor first with grenadier.
General strategy is try to locate that guy as early as possible/as late as possible. Avoid combat when distracted by other alien pods.
In addition, try to select non-timed mission when dealing with rulers.

That guy can do everything a normal Viper can do. Except for one Area of Effect frost breath attack that stun your troops for 2 turn. Try not to stand bundled together in a small area.
He also has high defense and dodge stats.

Use FROST GRENADE to stop that guy from taking turns (3 reaction)
The bowcaster shoot cannot be evaded, which nullify his dodge stat (but that weapon is pretty terrible tho)
The axe can be thrown, which does not trigger a ruler reaction.
Bring gas grenade/ fire grenade (damage per turn grenade in general). The rulers take damage each reaction.
STASIS of Psi OPS can stun that Ruler for ONE TURN so you can reposition or dispose of other aliens.

LOOT: SERPENT ARMOR - ENDGAME ARMOR - build from Proving Ground. Can be upgraded one time.
The armor is equipped with a hook (which does not trigger a ruler reaction) and a frost whip (frozen tatgeted enemy + pull smaller ones out of cover)
Cause 1 viper to panic each pod.

The strategy is the same. Make sure your will stat is high to avoid the roar attack of that guy. (cause panic and unconscious/ stun on low will soldier)
Lowest dodge/defense among the three rulers.
Use the ability of serpent armor in addition with those weapon above as well.

Gas grenade stun that boss for forever I believe. The AI is bugged somehow.

Loot: RAGE ARMOR. 1 SLOT of HEAVY WEAPON. Can be upgraded one time. Ability: Rage strike ( fast melee attack that does not trigger a ruler reaction or consume a turn )
Passive: make 1 muton or berzerker panic.

This guy is more dangerous than the other. He got one ability that rains fire from above (chance to stun/ unconscious, absurd Area of Effect) so try to battle him IN A BUILDING. The building's roof would take everything.
He also has extremely high dodge and defense.
Don't afraid of his grabbing attack. Just shoot him once and the grabbed soldier would drop to the ground safely.
Use the strategy above and the RAGE armor's ability.

LOOT: ARCHON ARMOR. ABILITY: TELEPORT ANYWHERE the character could see. Remove conceal. Recommended on Snipers.

Passive: Make 1 archon panic.