I tried before and after Hotfix 1.68. No problem on this side. All files were validated.

Are you running any mods ?

No

@razazel I think I found the issue. You can actually complete "destroy the artillery" objective without completly destroying the armor (with an RPG-42 AT rocket in the ass for example). But, later, the blackfoot will not crash until it's fully destroyed. While the helicopter was still flying around shooting at things (like in the video I linked) I destroyed the artillery with explosives and the blackfoot went to the crash site on it's own after a minute.

In fact, it seems the blackfoots are supposed to target the artillery if it's not destroyed in order to proceed to the crash site but despite they're firing a lot of rockets at it, the artillery doesn't explode.

It's directly linked with the 1.68 general problem of hit effects inconsistency.
Before 1.68, there were some logical links between calibers / armor / effects / HUD display (for hit points). The only damage global command was inconsistent as you obtained 0 for some cars almost totally destroyed by 7.62 (example).

Now, and probably due to the will to avoid systematic explosion when a vehicle is bullet riddled, there is a deeper step in inconsistency. Damage command is still useless for scripts, but also HUD displays are missing some hulls or guns hit points, some guns are staying operative when they should be destroyed. Example:
Just fire an AH9 at a prowler armed (with minigun 5000 "nullets") The hull is never hit (HUD) and the car never explodes). Then jump into the "wrecked" prowler, feel free to use its MK30 as it's like new (no hitpoint for prowler's gun), and return fire to AH9. It takes some time to hit all parts but the helo explodes. Minigun 0 / HMG 1.

See also https://feedback.bistudio.com/T124183