Gears of War 4

When playing horde you'll kill enemies and they'll drop these small glowing items, this is power for your fabricator (the blue box your team sets up at the start of the horde game).
This power is a special type of currency that it used to build fortifications, weapons and other buildables to help you beat enemies.

Now that you understand what you're collecting and its importance, let me tell you how the best way to go about collecting it.

Starters you'll want to be playing as the Scout. This class has a passive that allows you to get more power out of a single power pick up then other classes but only when the wave is active i.e. when enemies are still alive. It doesn't matter how many enemies are around so you can leave one alive and the boost will stay around. If it's the time in between waves when it has the count down timer and no enemies, you get no boost and at that point anyone might as well collect it.
Although you can get a skill that increases what you get when you deposit your power into a fabricator and this can be upgraded for a higher percentage.
Even with the skill boost it's still ideal to get as much power as you can when the wave is still active. So either by yourself know to go out and collect when a few enemies are left or coordinate with your team to leave one enemy alive.

The stronger the enemy the more power they drop. Bosses will drop over 1,000 power.
If players or buildables are destroyed, they will also drop power.
If you die you will drop whatever power you had and it will not count towards your progress on this unless you can collect it in between the waves during the count down timer. Your bonus from picking it up during the wave should still be there. If someone else picks up the power from where you died and deposits it, then you will also not get progress but they will.
Higher difficulties will get you higher amount power drops from enemies. On casual though in two games where I completed all 50 waves with my first game not using a increased deposit skill and the second one with a 30% increase, I managed to reach almost 50% progress on this achievement. (I was also working with/against another Scout player, had it been just me I'd probably be like 70% already but at least my team wasn't short power as some waves will accidentally get ended prematurely and less power[+the passive bonus] is missed if two people are actively collecting it.)

So play Scout and do your best, use whatever skills to help you and you shouldn't take any more than ten full matches at the most, maybe around four or five at the least. Obviously if you're not completing matches to wave 50 or somewhere in that range or people aren't cooperating and they're picking up power, than you're looking at many more matches.