Ok so this can be a very frustrating one but it's doable and no biggy if you're a patient player. I must warn you in advance that you'll NOT get this one right away as soon as you fulfill all the requirements because this achievement is bugged as the Digital Continue itself said so. But to amend this they have an internal update that runs every 10 days or so called "Cup of Drink". This makes the achievement pops for the players who did met the criteria but didn't get the achievement right away.
If you follow the threads here about this achievement you'll see a lot of players reporting they've done everything 2 or 3 times but didn't get the achievement but they all got it eventually once the update rolled and all they had to do was to be killed by a random enemy and the achievement popped.
In my case I'm positive I got killed by every enemy and died in all possible ways at least twice and still didn't get it. Then one day I accidentally got killed by a Topper and it popped even though I had been killed by it a hundred times before. So my advice to anyone attempting this one is to make sure you're killed by every common and rare enemy, ALL 4 bosses, ALL shadow enemies and the other factors on the list below. Once you're absolutely POSITIVE you've been killed by every possible enemy and died in all possible ways the achievement will most likely NOT pop immediately but since you know for a fact that you did everything right, my next advice to you is to start the game everyday and get killed once by any enemy. If the update was rolled recently you'll get your achievement then.
You see it's not a hard task but it'll require you to be patient. I personally was very anxious with this one because I knew I'd earned it but I still had to wait for an update to make it pop. And to make me even more anxious this was the last achievement left for me so I was dying to complete this game asap and move on to the next one. But if you're not the type of player that has an urge to see an achievement pop and you're cool with cheevs that pops eventually and don't keep thinking about it then you're fine.
Now one of the players here who was trying to get this one said on the threads that one of the moderators of the game told him that the requirements for this achievement are restricted to the main enemies only, both common and rare, no need to be killed by bosses, shadow enemies and other factors such as burning, poison, falling rocks, time and greed. Once again my advice is to cover all the possibilities just to be sure.
To increase your odds of finding rare enemies faster create your own venture and use the rare enemy generator. You can spend up to 9999 prestige to generate more rare enemies if you have enough money. I got lucky to earn a lot of prestige upon completing the 920 levels long featured venture created by AspyrBash and when I killed the boss my reward was 450000+ prestige so I had no trouble with money. Also always play on hard since some enemies on the list you only encounter on this difficulty.
Remember, the achievement can frustrate some players but it's obtainable, you just have to be patient. I hope you guys find all this info helpful, if you follow my recommendations here you'll absolutely get it eventually. Good luck!
And now with no further ado I present to you the complete list with all enemies you can possibly get killed by, including ALL 4 bosses, ALL shadow enemies and ALL randomly generated factors such as time, greed, falling rocks...
Just a quick heads up about shadow enemies: some of them can not be found on dark heroes levels so when you find an "Alter Echo" level die with your current character then go to the character selection screen and pick a new character and you'll face a dark version of this new character you just picked. Do this with ALL heroes before proceeding to the next level. Also for some shadow enemies the game will say "Killed by Mysterious Source" instead of the actual name of the character. They are: shadow Jett, shadow Morta and shadow Widget. I wanna thank My Name is BaRt for the list of enemies.
Spikes from the spiker