It sounds like a missing trigger point or Act = line.
This m02.ini excerpt is taken from the m02 folder.

[Trigger
nickname = give_up_cosmo
system = Li03
Cnd_HealthDec = PEscort1, 0.500000
Act_StartDialog = cosmo_giveup
Act_SetVibe = King, PEscort1, REP_FRIEND_MAXIMUM
Act_SetVibe = PEscort1, Player, REP_FRIEND_MAXIMUM
Act_SetVibe = PEscort1, King, REP_FRIEND_MAXIMUM
Act_SetNNObj = stand_down
Act_LightFuse = PEscort1, mission02_cosmo_burning_fighter_fuse
Act_SetOrient = PEscort1, 1, 0, 0, 0
Act_CallThorn = missions\m02\m02_cosmo_01.thn, PEscort1
Act_PobjIdle = no_params
Act_ActTrig = revert_cam
Act_AdjHealth = us, 0.750000
Act_NagOff = nag_battle1


=========================================
I'd start my search for something missing around there.
Of course if Cosmo dies, the mission is supposed to fail and you're supposed
to reload back to the point where you just enterend the Colorado System.

[Trigger
nickname = give_up_cosmo
system = Li03
Cnd_HealthDec = PEscort1, 0.500000
Act_StartDialog = cosmo_giveup
Act_SetVibe = King, PEscort1, REP_FRIEND_MAXIMUM
Act_SetVibe = PEscort1, Player, REP_FRIEND_MAXIMUM
Act_SetVibe = PEscort1, King, REP_FRIEND_MAXIMUM
Act_SetNNObj = stand_down
Act_LightFuse = PEscort1, mission02_cosmo_burning_fighter_fuse
Act_SetOrient = PEscort1, 1, 0, 0, 0
Act_CallThorn = missions\m02\m02_cosmo_01.thn, PEscort1
Act_PobjIdle = no_params
Act_ActTrig = revert_cam
Act_AdjHealth = us, 0.750000
Act_NagOff = nag_battle1

[Trigger
nickname = heal_cosmo
system = Li03
Cnd_HealthDec = PEscort1, 0.500000
Act_AdjHealth = PEscort1, 1.000000

[Trigger
nickname = cosmo_die
system = Li03
Cnd_Destroyed = PEscort1, 1, ALL
Act_ChangeState = FAIL, 21600

that's what I have in m02.ini so there's nothing missing I think...shoud there be some trigger that would make cosmo give up when his HP drops to a specific number? the problem is I can't even disable his shield...so there must be somthing rly screwed somewhere...I noticed that the exact thing happens if I try to destroy king in the same mission...I need sugestyions because I'm not sure where to look but if you tell me I'll know what it's about, cuz most of the freelancer inis are self explanatory so they're not too hard to tamper with.

A question comes to mind:
did you at any time use any mod that altered shields or included altered shields?

If so, unless you know where to start looking for those changes,
you're only option might be to completely uninstall the game,
then install the game again like you just took it out of the box.
Aside from that:
The only really easy quick fix I can think of in this instance
(since you've only reached mission 2) is to uninstall the game
and do a new install.

If you have used a mod before, I'd start checking in that mod folder where the
changes affected shields. In such a case, it could have also altered the npc shields in the story line. In effect, rendering the mod unusable in SP.

I am using the nearly invulnerable shield mod from the mod manager...that might be it...funny...I've been using it for a really long time and this is the first time I've had problems...I'll check it out and post if I find the problem or not...as for reinstalling the game...tried it...tried starting the game fresh with no savegames but still I have the problem...BRB I guess

I've used that mod before, but didn't have any related problems trying to
disable Cosmo during that fight. That's really odd.