Don't rush the kills. You want to kill ennemies when the breach is at level 1 or 2. When it is at level 2 and you have the choice to kill it or not, I suggest you to kill it only if there will be 2 or less person alive next turn if you don't kill it or if it will be too high in health.
When possible, split the damage by going to the same peril as a teammate. That make his attack be rounded down and make the armor of all players in the highest peril be utlised.
Upgrades - consider carefully which sheet you want to upgrade, and at which time. First sheet increases HP pool. Second sheet increases Armor. Third sheet increases XP gain for killing monsters. You usually want to upgrade your third sheet once early (level 1 or 2) because it increase the gain of xp per kill from 1 to 2. If you didn't upgraded it, you have the possibility to never upgrade it the whole game.
Armor: armor is usually not good. It's positive don't get me wrong, but you don't usually upgrade a card for it's armor (check one exception right below). But against some enemies (gain hp equal to damage dealt & reduce healing by half), this is absolutely great.
Hp: upgrading hp and armor can be used to survive the following round. This require concentration each turn but can be really powerful.
Stargazer:
This character is the hardest to play. You want to upgrade it levels 3-2-2 (or 2-2-1).
Sun give you more damage, moon give you support.
The 4 dice is the most powerful by far. It let you give experience to others. Upgrade it first and spam the sun of it. For that reason, you don't want to goes to moon early.
You usually want to stay sun to be able to deal damage if needed. Exception being at the start of a fight where being able to play a 2 early can reduce the attack of an ennemy by 2 which is great.
Upgrading the second sheet let you be able to heal others. In rare cases, that can be great.
Death strider:
This is the second hardest character.
The most powerful ability is the 6 maxed. It let you do 3 damage to yourself and deal 6 damage to the opponent. The problem is that it require ton of xp, and in many games you can't rush it.
Alternatively, you can upgrade the 1 ability which is the main utility since he deal ton of damage.
When you got heal, try to stay at a number of wounds equal to the 1 ability.
The 4 ability is meh, but again some ennemies make it great.
Commander:
This character add complexity to the whole team.
His 6 let you use the 6 ability of others, which increase the value for the other player to upgrade their own 6.
Hunter:
The best character. His most powerful ability is the 4 which increase the breach. Upgrading it once is great.
Then if you get 12 more xp you can upgrade it two more to instead of making it gain 1 attack will make him lose 1 attack. But in my opinion, it's usually bad. If you roll that 4, you will get more turns to kill the ennemy, which mean you are already in a good shape. On the other hand, if you don't roll 4, you will be in a pretty bad shape, especially if the team spent ressources to upgrade that 4.
Medic:
Medic work pretty well with low and high experience.
With low experience, you got access to a debuff with 2, and an aoe (area of effect) heal with 4.
With high experience, you got a 6 which can heal for 4 which is great, and a stronger debuff with 2.
Sensei:
The second best character. He gives experience to everyone.
Level up first and third sheet to gain the most experience and be able to level the whole team.
It's often a good idea to give him experience early to make him be able to give that experience back faster.
Lancer:
Soon.
Blood mage:
Soon.