How to defeat the Archon ?

Are you sure you mean the Archon?

I think they mean the Cardinal on Voeld after the 'prison' break.
That's just a guess though.

Humpf. Judging from this post, this guy is only trolling around. Maybe I'm getting it wrong, but...

Are they twins. It seems easy to kill Archon after beating the Cardinal. Not sure why ?

With Singularity and Lance it is possible to get Ascendant stay down for a while, then one can shoot it and use lance again. The trick here is singularity explosion variant. Shoot orb until last millimeter of health, launch singularity, shoot if necessary * orb explodes * -> lance -> disable singularity (it explodes) -> Ascendant flies to the ground -> shoot -> lance -> shoot until it dies.

Other method I know is to kill the Orb and use Snap Freeze on Ascendant to get it drop down to the ground. Same rules apply.

In multiplayer I use Commandos Warp after singularity.

I just shot at him and not his head or his orb. And he died. It took a while but he still went down. I am not sure as someone said that first shoot at the orb, then shoot at his head in two big steps. Both are difficult to do. Not sure it is the right way.

You have to take the shield down before any shots will do damage to the Ascendant's health.  Head shots will do more damage than body shots in most games and ME:A is no exception.  The "orb" is the head shot equivalent for the shield.  If you shoot the orb, you do more damage per shot to the shield and it will go down quicker than if you just generally shoot at the shield.  Similarly, if you shoot any enemy's head while their shields are down, you will kill them with fewer shots than if you just shoot their body.  If you're using biotic powers or power combos though, that's a completely different thing.

Doesn't it depend on how good you are at aiming a sniper rifle quickly?  The shots that hit the orb and head will consistently do more damage than the shots that miss.  You can play any game using the straight "spray and pray" method and eventually the enemies will go down.  If that's your play style, play it that way.  Me, I prefer something more precise.  How many shots you take depends on what exact gun you're using, what level it is, how is it modded, how have you allocated your skill points, and what difficulty level you're playing at.  If you're claiming to have taken down an Ascendant with 3 shots without hitting the orb or the head on any Normal or above difficulty, I'd need video to believe you.

I got caught by an ascendant 2-3 times.

This is true.  I've found that Clancy on Eos quite often has one in his inventory though.  Once you establish Prodomos, the vendor there also occasionally has them for sale (although not usually as frequently as Clancy).