Saints Row

Faction minibosses appear once you've reached level 5 notoriety with a faction. They're marked with a red skull on the minimap and killing them will clear your notoriety. If you do the loyalty missions and main missions, you'll receive this achievement with normal progression. This achievement requires a miniboss kill for Los Panteros, the Idols, and Marshall. You do not need to kill a police tank for credit.

If you'd like to get the achievement early, you'll need to build notoriety to attract a miniboss. To do this, you can attack a gang member and allow them to call in reinforcements. Keep killing each wave of enemies, but leave at least 2-3 alive so that more reinforcements are called. If you kill everyone, your notoriety will decay and clear pretty quickly.

If you have unlocked criminal empire level 3, you can build the KAKTS radio station, which gives you the ability to call a gang to come attack you. You'll immediately receive level 3 notoriety and it's fairly simply to build up to level 5 from there. When you call a gang to attack you, you don't have to worry as much about leaving people alive. Waves will spawn until you leave the area or kill the miniboss.

The minibosses for the Idols and Los Panteros are fairly straightforward. They're heavily armored, but they can be brought down like normal enemies by shooting them or using explosives.

The miniboss for Marshall is a guy in a mech suit and he is invincible. To kill him, you have to let him fire his weapons at you until they overheat; when this happens, he'll open his shoulder and back plates to show bright green rods that you'll need to shoot. Shoot the two shoulder rods and then go behind him and shoot him in the back rods. Shooting the back rods will lower his armor and eventually kill him. You're on a time limit because he will eventually close the plates, hiding the rods, and start shooting at you again. You may need to do this a few times, but you should be able to kill him in one round with a powerful level 3 weapon.