Atomicrops

The elite enemies are the ones that have an orange glow around them and they will either summon flying skulls or shield other enemies.

They will appear staring from Year IV and more of them will spawn on later years. I did this on year VIII and found exactly one elite enemy in each biome.

The ingame description says to kill 6, not 25. 6 is the correct amount, but they need to be killed in 1 day and without taking damage in between. You can take damage before you kill the first one.

The swarms of bats and pterodactyl count as only 1 enemy.

To get the achievement clear the biomes like you normally would, but when you see an elite enemy stay away from it's camp and try to remember it's location. Once you've discovered 6 of them, complete your day, make sure you are not on a day with a boss, buy and upgrade a good weapon and start the next day, rush towards the elite enemies and kill them without taking damage and the achievement should unlock.

If at any point during your attempt you mess up, you can hit the xbox guide button, turn off the game and boot it up again and you can continue from the start of the day you were at. All the elite enemies will still be in the same location, the only thing that changes are the 2 random guns you have and sometimes the upgrades you can buy. You can also exploit this, if you don't get the weapon you want.

As for the character, I used Thyme, because their longer days make it much easier to clear the biomes and still farm enough to buy good weapons.

even start from year 4 elite enemies will appear.
but the amount is not enough to 6.

recommend do this in year 6.
each area exactly have 1 elite emeny. no more no less.
find it, mark the psition, and skip it for now.

after you found all 6 elite enemies, wait until end of the day.
first save and quit then resume game

start hunt them down in 1 day.
if you get hit, pause the game, and use xbox dashboard to quit the game.
after resume it will back to town with your last save.

try it again until you beat them down