Early on you won't be too hard-pressed for fragments to ascend your heroes. However, by hitting tier 3 and heading for tier 4, the number of fragments will rise dramatically into a whopping 80 for each fragment (and when you aim for tier 5, it turns into 280 per). To make the most out of your Upper Dungeon farming, buy Loot Boosters with your rubies, and stockpile an extra 600 rubies. Thats a total of 1100 rubies worth. Then, when you are at 11;30pm, use your loot booster and roll into the upper dungeon. It takes about 2 minutes per run if you're at the exact right level to clear the map, so you can do 5 runs in 10 minutes. Recharge 5 runs for 100 rubies, repeat. Recharge for 200 rubies, repeat. Now you should be hitting 12:00am of the next day, and have 5 extra charges. Do 5 runs, recharge, repeat, recharge, repeat. You can do 30 runs of the upper dungeon within the time limit of one loot booster and maximize your output this way. If you're max farmed on tier 4 items and levels, and aiming for a 5 star hero, the chapter 4 Upper Dungeon yields about 7 drops per run which turns into 14 with a loot booster. Thats 70 fragments per 5 runs, and 420 fragments in a day. Thats 840 in 3~4 days for 2200 rubies, more than enough to raise 1 character to a 5 star from 4 star.