Sentinels can be obtained by either spending 75 Platinum in the store, or buying the 100,000 Credit blueprint for one and then gathering all the crafting materials,
So the fastest way unto this achievement is to buy the $5 Platinum pack and then purchase a Sentinel.
I used Dethcube for this achievement.
They level up like anything else, you bring them with you on missions and they help you in battle.
As for leveling, for every kill the Sentinel gets it is awarded EXP and also gains EXP from acquiring affinity. (Rewards for completing the bonus challenges that pop up during missions. "Get 30 kills with a pistol" "20 Melee Kills," etc.)
The fastest way to get their EXP is to let them get the kills. Since they don't get "Assist Experience" or anything like that. I recommend playing a Defense Mission and farming.
*Plus, using Dethcube increases progress for
Two birds with one stone.
Hope this helps!