Do you enjoy the puzzles you run into when playing with water's movement manipulation system (Swap, Nixie, Thin Ice, Troll Bridge)? How about combining those effects with an avatar that can fly any type of unit? Mist AoA keeps the board as dynamic as possible whether it's flying opposing minions into traps, flying your minions out from the backline for safe setups, or flying your minions off the frontline for aggressive pressure.
The ideal opening includes at least one defensive site (Bottomless Pit, Thin Ice, Troll Bridge) and at least two air sites (one for your starting site and one in the second row). This gives you two prime locations to use AoA's ability and somewhere to send opposing minions. With Perilous Bridge, Wuthering Heights, and River Rapids, this deck can funnel opposing minions into either your defensive sites or your flight-ready air sites. You won't always have an incredible defensive setup, but when the cards come together right and you know what to set up, it can seem unbeatable.
Being able to fly yourself / minions without needing to step first is essential, so always mulligan towards an air site to put under yourself. For your second site, prioritize any of the aforementioned sites depending on the matchup, all of which can be happily played in front of you. If you aren't playing an air site in front of you, it's fine to wait a little before playing an air site in the second row. Try to get it down on either side of the site in front of you, since you can fly yourself directly there, but it usually isn't a big deal if you lose access to those locations and need to develop a little wider.
It's rare for me to not play a site in front of myself with this deck, but there are certain matchups like Battlemage where I never want to play in front of myself, or water matchups where I want to see what my opponent plays in the middle before I play there.
Ideally, your air sites will be in throwing distance of a good defensive site and you won't have any weak sites exposed. Look to avoid playing sites in locations that may become hard to defend. If your opponent presses into you with their sites, it actually won't help them much when they're next to your defensive sites and air sites. So don't put weak sites in the middle to lock in territory. Putting weak sites on the back row is fine, and you can summon minions nearby to protect them when needed.
This deck plays ~17 four-power minions, combining them with Trinkets and Whirling Blades to answer opposing minions. The Daperyll Vampire and Renatus are usually best played on the back row, farther away from your opponent, but there are definitely situations where you can risk summoning them in the middle of the realm.
With Hyperparasite, try to set up lines where you fly it and then pick something up. Hyperparasite has a few rules to keep in mind. He can't pick up stealth minions, since picking up requires targeting, but he CAN pick up warded minions, since picking up is a basic ability, and wards don't apply to basic abilities. Once the minion is disabled, the ward breaks. Minions being disabled by Hyperparasite are great targets for easy attacks, but be careful about stacking your minions on one site. Consider when it might actually be better to not attack a held minion, applying more pressure while risking the held minion becoming un-disabled. Remember that you can only pick up and drop once per turn each, and you can't drop after striking.
These are all about timing. "The best brainstorm is the one you never cast." This wisdom highlights that the more powerful a spell is, the more value you can get from it by waiting for the right opportunity. Look to Swap enemy minions onto defensive sites, like Swapping an airborne minion off of a Bottomless Pit to kill an opponent's non-airborne minion. You can also Swap a minion you control from AoAs location with your opponent's minion, then fly their minion somewhere bad. Because Swap has so many possibilities in this deck, try to hold it in your hand as long as possible. A better possibility will probably come up, unless you already have a really good one. Don't be afraid to try using the non-minions in experimental ways. They offer a lot of flexibility and your creativity will be rewarded with opponents never seeing your plays coming.
It is often good to fly forward one diagonal step as early as possible, giving you a roost to send out minions aggressively. In other cases, you will spend more time roosting on the back row. AoA gets interesting when you start pivoting between these two positions, planning out future turns as you move between them. Sometimes you will steamroll an opponent, flying yourself into the third row to launch minions from up close. Once your opponent is getting close to death's door, don't be afraid to leave your air site and start attacking with your avatar.
The mana curve is designed to maintain a high average card quality while being capable of using the majority of available mana. (There are certainly situations where it's better to not use mana and save cards for opportune moments.) The deck is well equipped to have games where it doesn't draw a single site for turn, curving out slowly when a matchup requires the boost in card advantage. But most of the time, drawing one or two sites for turn is advantageous to increase the stream of pressure. AoA likes to get involved in the realm with steps and attacks, so hitting 4 or 5 mana at a quick pace frees her up. Keep in mind that drawing sites earlier gives you more information and more control over how the sites in your hand get arranged on the board. If the sites in your hand are self sufficient, it's usually best to draw additional sites as late as possible, picking up spells earlier so that you have more information and options with those instead.
Bottomless Pit with a dual land is usually keepable, but without a dual land it's worth thinking about the risks. Keeping a Pit with a River Rapids or a Wuthering Heights is strong in most matchups, but must be weighed against threshold risks. This deck relies on using cards precisely and resourcefully in order to make up for the risks of having the wrong thresholds at the wrong times. Usually, you have enough cards to overcome the variance.
When it comes to spells, I keep it simple. I mulligan anything that costs five or more (unless it's critical to the matchup), I keep no more than two four-drops, and I keep no more than one non-minion.