Diablo III

To get this achievement you must complete these three challenges

Uncaged - Kill Diablo without getting trapped in a spike trap and without dying on Hell difficulty or higher
While fighting Diablo will sometimes have glowing hands where it looks like a spell is going to be casted after a try or two you will recognise when it is about to happen which is your queue to roll or run out of the way. This can be tricky to dodge, and may take some practice, but having co-op allies to help distract or stun her can beneficial.
I did this several times and it wouldn't give it to me then I tried getting rid of my follower as they get caught in a spike trap on the way to diablo so think you need to go there solo

Self Sufficient - Kill Diablo without using any health globes or healing wells on Nightmare difficulty or higher
There are some healing wells located in the main boss room, and Diablo and the shadow clone will also drop health globes from time to time during the fight - avoid both. You can still use potions if needed but if its set to easy you shouldn't need to. You will also need to swap out any armour or items that pick up gold/health from a distance as you will pick the orbs up without even realising. As pointed out by N3m3si5 you can use health potions

There Can Be Only One - Fight and kill 5 clones of yourself in Diablo's Realm of Terror on Hell difficulty or higher
During the 2nd , you will be in a shadow-world where you must fight a shadow Diablo and clones of yourself this will need a couple of attempts, as you will only fight 3-4 per boss fight but they do accumulate over so just go back through quest select and kill more

To get Self Sufficient, have a friend or two in co-op do the fight for you. You take off all of your armor and you will die in about 1 hit. Just stay dead the whole fight and you will get the challenge when your friends kill Diablo.

They can heal and pickup orbs all they want, as long as you do not heal. You can't heal if you are dead!

Not a solution so much as a note for Monk users. Summon your spirit ally and let it do all the killing. It won't pick up orbs, so all you have to do is stay out of the way.

Just giving a tip for getting Self Sufficient those playing as a barbarian and maybe others but I'm not sure about their move sets so can't say for sure,

Do it on Nightmare and Easy, as said by others unequip stuff that increases pick up range but for this it should not matter, the fight will be over in seconds, the part that was giving me issues was the section in the shadow realm where Diablo summons clones of you, as a Barbarian ir was very difficult to kill them and not pick up the orbs they drop.

Here is what to do, equip the ground stomp skill (X button) and as soon as you gain control in the shadow realm nail diablo with it before he vanishes, this will stunn him and allow you to kill him before he can summon the clones!!!!!!

If others classes have a similar move that stuns then it might work for them too, but as I said I haven't played them yet so can't say for sure if they do.

Self sufficient tip to make it easy :

Nightmare mode on easy, remove any gear with pickup range.

I removed most of my legendaries, including pants, helm, gloves and boots. I pretty much did it naked bar weapons.

Now, real easy and simple. Use skills and meeee attacks, but after every melee swing, just roll away from diablo or the clones and you won't get the health orb.

I still killed him real quick, and had rend with the healing rune just in case (wasn't needed).

Basically, melee then roll, melee then roll etc. as the boss is only low level if your 60, makes it a cakewalk!