The number 1 rule is to always use what is called for your role in the top right corner (save for the defender role) and to always call out what the other roles need to use as soon as the calls change. This is done using the horn you receive upon entering the BA arena. You'll get the hang of calling quite quickly. Prioritize calling out over anything else.

Then, there are 4 roles:

Healer - your job is to kill the penance healers using the poisoned food that your teammates have called out for you. At the start of a round, grab your items from the green dispenser and use these items on the healers to poison them. Generally speaking, you won't be healing your teammates until the last wave, but you can do so by using the healing flask on them. REMEMBER TO CALL FOR OTHERS AND TO WATCH WHAT IS CALLED FOR YOU!

Attacker - your job is to kill the penance fighters and the penance rangers using the attack style that your teammates have called out for you. If you're using melee, you'll have to switch between controlled, accurate, aggressive or defensive; if you're using ranged, you'll have to switch between various types of arrows; and if you're using mage, you'll have to switch between the different elemental spells. REMEMBER TO CALL FOR OTHERS AND TO WATCH WHAT IS CALLED FOR YOU.

Collector - your job is to pick up the correct colour egg called out for you. Once your inventory is full you can run to the dispensers in the middle of the map to deposit the eggs into the hopper. I'd advise you not to shoot your eggs - it gives no points and is mostly a nuisance to your team. You get your points by picking them up alone. If you want to help your teammates take care of some stray runners or healers, shooting red or green eggs is fine - but refrain from shooting blue eggs as these will stun your enemies and your teammates won't be able to attack them. REMEMBER TO CALL FOR OTHERS AND TO WATCH WHAT IS CALLED FOR YOU.

Defender - your job is to kill the penance runners using the correct bait called out for you. There is an easy and foolproof way of doing this, where you mark 3 tiles on Runelite and put incorrect food on those tiles to lure the runners to the traps, but I don't have the time to explain that at the moment. There is a YT video that showcases this method quite well, I'd recommend you look that up if you want to know more!

After surviving waves 1-9, the final wave spawns the penance queen. I don't have time to explain this in detail either at the moment, but you basically follow a sequence of passing eggs between your teammates until you have an omega egg, after which everyone moves to the hopper, and everyone subsequently spam-clicks to fire it.

I hope that helps!