I just reading some of the comments and I realise how lucky I am. My first adventure gave me the first egg. Then the 7th and 8th one gave me the two remaining eggs!
Oh before i forget just some tips and theories i use for a long long time
..........maybe it's just superstition but the game seem to give way better stuff when:
1. When you have a full inventory. Let just say you have 99 Stones, 99 Iron Ore and 99 Coal but not 99 Jewels, Silver or Mithril. When I collect from the Deep Mines or Mines, the Mines seem to give me way better resources (more Jewels, Silver and Mithril) then when I don't have 99 Stones, Iron Ore or Coal. The (Deep) Mines will only give me Stones, Iron Ore or Coal but no (maybe 1) Jewels, Silver or Mithril when i dont have these resources maxed out (Stones, Iron Ore and Coal)! I only get adamant from the Deep Mines when my inventory is full of Stones, Iron Ore, Coal, Jewels and Silver! (because the total of 15 adamant i recieved from the deep mines only came when all those recourses where full in my inventory) The same thing works for me with all the other collectible buildings: Sawmill, Hatchery, Stable, Sir Pigglesworth, Ivy's Hut, Dragons, Ponds, Rustic wells (I get more Mermaid scales when water is full in my inventory and less Mermaid scales when my water is not full), etc, etc even Adventures!
2. I get way better resources when I don't do an adventure everyday!!!!. When I do an adventure everyday after 5 a 6 days the adventures seem to stop given me any good resources or special items, but when i stop doing adventures for let say 1 or 2 days and then after that i start an adventure the first one seem to give me good resources and special items. I did about 20 adventures in a row and didnt get any good resources or special items (item boxes) So I stopped doing adventures for 1 week then started again the first adventure gave me my 7th Alicorn Horn. Then I stopped again for 2 days started a new adventure after the 2 days and that adventure gave me my 7th Alicorn Wing. I get way more item boxes or special items from adventures when I take breaks between adventures for 1 or 2 days instead of doing them in a row (everyday)!
3. Again maybe it's just superstition but this works for me!
Last but not least doing the famous collecting trick in your Kingdom seem to give way better resources and items too. So when you click on let just say +/- 30 a 35 buildings (buildings or collectibles in your kingdom) (make sure you click on your best buildings as the last ones, like the Deep Mines, The Keep and Barracks etc) and do the collecting trick, all the resources and items pop up directly. I manage to get 4 (normal) dragon eggs, 3 Manticores eggs and a lot of Alicorn Horns and Wings this way!
Just like the 3 Special Dragon eggs,I waited for some time between the adventures. And when collecting I click on several buildings very fast (the keep and barracks as last, so they dont get colleted before the trick) then i did the collecting trick and got all 3 special dragon eggs this way!.
I hope these tips help all of you who still searching for the eggs! So when you decided to do the Infiltrate the Pyre Caverns adventure for the very last time just atleast wait for 3 or more hours before doing an adventure again (3 hours because the Infiltrate the Pyre Caverns adventures duration is 3 hours, when doing a 22 hour adventure wait atleast 22 hours). Who knows...maybe "the game" really thinks you gave up but then after the waiting time "the game" maybe will reward you for your determination, consistency and perseverance.
Good Luck To All!!!!!
ps Im sorry for any spelling errors or mistakes, as you already noticed, English is not my first language