Rank as high as you possibly can in the arena. The first benefit is obvious – you earn more crystals every week, which will allow you to purchase more mystical summons. However, once you hit 1,500 points/rank of 2000 or less, a serpent will start being included in with your rewards. If you manage to attain rank 1, a four-star succubus will also be included in your rewards.
Some of the awakenings of monsters, oddly enough, actually will change their star rarity. For example, if you awaken a low elemental of any color, they will turn from a one star monster into a two star monster. This is true for other monsters, too, and sometimes, you’ll even add TWO stars onto a monster’s rank by doing awakenings.
Summoning pieces will earn you rare summons, depending on which pieces you get. Go to the Cairos Dungeon and look around the item drop info to figure out which dungeons provide summoning pieces as a reward. You need to get a certain number of one summoning piece. Once you get that total, go to the summoning area.
Once you’re there, scroll all the way down to the bottom summon. Pick through all of the summoning piece types that you have until you find the one that’s complete, then go and perform the summon.
The thing about Cairos, though, is that loot drops are NOT limited to what you see on the item drop screen. Oftentimes (not so much in the hall dungeons but in the other ones) you’ll get random drops that have nothing to do with what you actually see on the item drop info screen. Oftentimes, yes, these can include troops that are 3-stars and above.
With the Arena, though, always make sure to set the strongest defense in your Summoner’s Tower, and to maximize your total number of Arcane Towers. The more of them you have, the more likely it is that players who attack you will lose. When they lose, you will earn more points and more glory, meaning that you will earn even better rewards (possibly including rare troops) at the end of the weekly period.