How long does it take you to acquire 20 Zetas?

Strategy? It's mostly about being lucky with the challenges and winning in fleet arena. There are weeks with no zeta mat dropping from dailies but from own experience I'd say the average is sligthly above 2/week. If you manage to rank 1st during your fleet arena payout consistently (and don't buy anything else from fleet store) you can get a zeta mat almost every day. Add another 1-2 from login rewards and you end up somewhere around 35-40 per month without Territory War bonus. Those could add up to another 12 zeta mats per month if you are in a very high GP guild that wins all the time, yet, that is not a realistic scenario for most players. Two weeks for a zeta as Grimstoned posted is realistic for someone that ranks high in fleet arena.