Probably one of the most sought after activities in HS is bossing. While for the lower lvl ones it is as easy as point and shoot, for the big bad ones it require alot of coordination and every group member needs to do his job at the right moment.
For the brood bosses and up, you want to bring along these chars and act as it follows:

TKR
Your key group member, most of the times makes the difference between victory and defeat.
Has to:
- always keep group buffed ( augment and preferable might too  )
- yank group or dead members back into fight
- decelerate boss and surrounding mobs ( key debuff )
- weaken boss
- heal merc / engies and anyone else who needs it

Engineers
Them on second position as need for bossing, same as TKR they make the difference.
Has to:
- focus on repair ( even if no crew, as long as the target is repaired and kept alive, you have a chance )
- heal whenever possible, if not , keep repairing

Mercenary
As of now, it is needed only for high lvl bosses, mid ones are doable without a merc, still for the new formed groups it is a must.
Has to:
- be able to stay alive as long as possible ( keep retreat and sustain on at all times )
- provoke boss and surrounding mobs at all times ( keep them off your engies  so they can do their job )
- heal self or group members when needed

Pyro
Your preferate damage dealer, the quicker they dish damage out, the less work for others.
Has to:
- always cast amplification aura before major buffs
- when shields down, cast decimate till out of psi then fire bolt or wait for more decis
- heal merc and engies while psi is building up

Path
Excellent for more dmg, debuff and crowd control.
Has to:
- always cast compromise on boss , sometimes makes the difference for all other group members' casts to land , less resists
- stun additional mobs till group can take care of them
- psi regen all psi classes
- heal merc and engies when needed

Smug
Excellent for more dmg, can hold aggro while group recovers if needed.
Has to:
- time ambushes right, preferable with obfuscate on, as it will draw alot of aggro
- obliterate boss when TKR is busy and can't cast weaken
- impede boss when TKR is busy and can't cast decelerate
- take additional mobs off engies when needed
- heal merc and engies when needed

As long as every member keeps an eye on everyone else and cast accordingly, there is nothing that can go wrong. It is advised to have at least 2 engineers in group, makes life easier.
No AFK accepted during fight, when people ask or demand some action, do it ASAP. ( most probably you'll see people shouting "heal / rep / debuff / mob". )

After boss is dead, it is preferable to share loot on a need basis. ( Even tho we all are greedy, including me )
Eg. if TKR needs that sa20 malixs to improve his overall survival, give it to him. Gear up the chars in the same order as listed above.
Try to build up the ship armor of all group members, it is the primary stat you're looking after.