All you need to do is take every dragon discover option you get. Of course it's rng stacked on top of rng stacked on top of rng, but each discover has a chance of winning you the game right away, so you're just forced to do it this way. The arena where you couldn't generate 10 cards every match was much more fun to me. Now if you don't get enough dragon discover, you just pray your opponent doesn't highroll. This is not healthy gameplay if you ask me
I did a couple arenas for the first time in awhile, and hadn't played this meta yet. I went 7-3 in both of them and every loss was to dragonqueen alexstraza or twin tyrant, with roughly half discovered by something else. Twin Tyrant should be nerfed; he's just got too strong an effect attached to a huge body, and he's often something like 3 or 4 to 1 card advantage as a result. Nerfing Twin Tyrant's health to something like 4-5 would at least keep him from being an almost-flamestrike plus 8-12 face damage and/or trading with 2-3 more minions/spells. Even a 4/4 Twin Tyrant would be very playable, though; he probably needs all his numbers adjusted to find some sweet spot where he can exist without being OP. 4/6 deal 3 damage to 2 targets or something... I'm not sure the exact numbers that would be best for him, but he's definitely a card that should've been playtested, because he clearly wasn't.
I have no idea what to do about Dragqueen Alex in the arena, though. In constructed, it's not a problem, but in arena it's just one of those 'oops I guess I can play bad all game and topdeck it and win' cards. Banning it in arena is probably the right solution, since I can't think of any reasonable changes or nerfs to it without damaging constructed.