For example, I played Pillar of Flame. Then the Pillar of Flame goes to stack. The "Whenever you cast an instant or sorcery spell, Blistercoil Weird gets +1/+1 until end of turn. Untap it." effect will trigger and will go to the stack. Then I will copy the Pillar of Flame via Dual Casting. The copy then will go to the stack. Then I will let triggered ability of the Blistercoil Weird resolve for it to untap. Then I will copy the original Pillar of Flame. With this, I have an original Pillar of Flame and its two copies on the stack and let them resolve. The Blistercoil Weird will no longer untap unless I cast another spell.
Is that possible?
Yes, that works just as you stated. Players get priority between each thing resolving on the stack, so you could create the copy, then resolve the Blistercoil's trigger, and create another copy.
So, after copying Pillar of Flame the first time, it must resolve then the Blistercoil trigger can happen to enable a second copying. It took me until writing this down to work that out, thought I might clarify.
Trying to work out how you resolve the untap from under the first copy...
I could be wrong but the Legendary rule is a state-based effect so would having two copies of Linessa is play for any amount of time would kill them both before you could bounce either of them, I think.
Hmmm...something has just occurred to me. How about putting it in a deck with Quicksilver Amulets, plenty of big creatures (e.g Vengeful Pharoah, Rune-Scarred Demons)? Add some Ponders to ensure you're getting what you need.
You can then either use the Amulet to cheat the big creature or, if the Amulet is dealt with, Ponder for another one and mill it for the Mindshrieker?
The way I went about this was making the big creatures still useful early game, Chancellors. 4 of each, 4 mindshrieker, 4 amulets, 4 Civiled Scholar), and 4 each of Think twice and ponder, with 20 islands.
Playing this, I once found a turn 3 win using the tangle mana to play mindshrieker first turn, accidentally finding chancellors while milling for it and having a little hasty goblin and 3 dross damage doing some work.
So, after copying Pillar of Flame the first time, it must resolve then the Blistercoil trigger can happen to enable a second copying. It took me until writing this down to work that out, thought I might clarify.
Trying to work out how you resolve the untap from under the first copy...
The way I went about this was making the big creatures still useful early game, Chancellors. 4 of each, 4 mindshrieker, 4 amulets, 4 Civiled Scholar), and 4 each of Think twice and ponder, with 20 islands.
Playing this, I once found a turn 3 win using the tangle mana to play mindshrieker first turn, accidentally finding chancellors while milling for it and having a little hasty goblin and 3 dross damage doing some work.