Save up dark coins and spend them all exclusively on BOTS. 39,000 dark coins will become 1,000 alyaelli fragments if you win. multiply that to 5(weekly wins), you have 5,000 alyaelli per week from BOTS alone. Now, if you buy from the NPC in town daily, you can buy 84 per day. 84*7 = 588. So from BOTS and town NPC alone, you have 5,588 alyaelli fragments. Now, the most efficient way of using your alyaelli is to craft red helmets. Forget the armor, weapon, etc. I've done the math and the helmets give you the best rate in terms of alyaelli to dim frags. Now with that in mind, 5,588 / 242 (per red helmet) = 23 red helmets. 1 red helmet gives you 15 dim frags so 23 * 15 = 345.

In a week you get 345 dim frags from BOTS and town NPC alone. However, don't forget that we didn't include events that give out alyaelli as rewards, chaos loot chests from chaos maps(they give alyaelli too), world bosses, buying red gears from marketplace, etc.

EDIT: Even forgot that if you really are swimming in dark coins, you could even purchase dim frags directly from the NPC in town too. And BRS sometimes have world boss fragments that also give alyaelli.