Upvote:2
Generally, no.
So putting a duty to check visa on the airline or travel agent would force them to be much more careful in what they sell to whom. Either prices go up as they figure the cost of problematic sales into their business case, or people with less-than-perfect papers will not get tickets, or both.
It would have to be something in domestic Vietnamese business regulations to support your claim, not in international air travel regulations.
Upvote:8
Is there anyway I could fight for this, and make them responsible for my loss?
Unlikely. Knowing the visa rules and having the required documents is in fact your responsibility. The terminals should have been listed on your itinerary. Unless this information was unavailable to you until check-in (unlikely), you're out of luck.