Just keep on it. They come - eventually, in (usually very) small dribs and drabs. Alpha only gems take the longest. You may well need 100's of them, all told.

Be prepared to spend months filling out all 12 - at least, in the mean time, Alpha's are as good as it gets (non-battle wise) for event points - and give your mates something to harvest, almost duplicating the total points effected for killing an Alpha in the first place.

And ... you will want the gem dust for the Citadel. [Just make sure you keep what Leprechaun's Heir needs, before sending it up to the Citadel.]

And don't forget - the harder the hit, the better the drop - especially along the way. So make sure you have Savage gear on, and may as well be applying Increased Hero's Offense.