I've found these to be fairly easy, but I'm just playing on normal difficulty at this point.
When the head or leg conduits are visible, shoot them. It doesn't seem very important which gun you use, but I like to use big damage single-shot weapons like the Carnifex, especially on the head. Shooting directly into the red on the legs or the center of the head gives you a weak point bonus, like a head shot. You can use your powers and combos on them as well. I found that, despite not actually lifting the conduit, Pull / Throw works to set off combos, although it doesn't stay primed for long. I was able to defeat the architect on Elaaden using only Pull, Throw, and Energy Drain, without shooting at it.
If you continuously move in a circle around the architect, outside the legs, it will almost never hurt you at all. Whenever the big red attack is about to go off, just evade in the direction you're already circling and it will miss. If you switch directions to try to go back, you'll end up walking into its targeting area, and probably into the nasty electric field it leaves behind. The biotic blink from the Explorer perk moves you further than regular evades, and I've found that it moves me far enough I can usually switch direction without getting hit. It also makes it easier to continue circling in cluttered areas without taking your eyes off the architect.
This can be complicated by environmental concerns, like the cold on Voeld.
When the conduits aren't visible, kill the Remnant it spawned. This is a good time to look for ammo, restore your life support, or get back into good position for another strafing run when the Remnant are dead.
If it flies away, chase it, but try not to end up directly under it when it lands. That can be painful.