Hired Gun or Han Solo. Second chance just keeps them around. It even has the added benefit of working around overkill damage.

Any helpful tips for going up against it?

Don't kill the 2nd chance character until you've got enough to finish them then do 5 more in a single turn.

If, for example, you get them to 1 health then all you need to finish them is a 1 damage, a 2 damage and a +3 damage matching the 2nd source of damage.

Your own board state ultimately decides how viable this is.

What about bypassing it and going for a mill strategy?

You've pretty much just got to accept Second Chance, and either try to eliminate yellow characters before they can get it out, or be prepared for additional health. Realistically though, it's not that much different from other things you've got to deal with - lots of shields, healing via Field Medic, trooper coming back with Endless Ranks. You've just got to be prepared for it.

Mill is of questionable viability, even in dedicated mill decks, because of their slow speed and the need to have discard effects . Without discard, you can mill their deck but you can't actually force them to discard from their hand, so you can't win that way.

I just noticed the battlefield for Han's freighter (Eravana) has a claim ability to get around this. Claim, switch second chance to another of their characters. Go first then kill the character off. They still have to have a second yellow character though.

Seems too situational.

Actually, claiming Eravana does allow you to get around this - the 'Yellow Character Only' requirement is purely when the card is played, it can then be moved to any character (Also, added hilarity - this means Obi Wan can have Second Chance). Of course, in this case, you've still got to deal with the other character having Second Chance at some point.

I see a lot of players lump all their dice of one type together and resolve it all at once. One thing which can help against Second Chance is to remember that you resolve dice one at a time (except for modifiers). So if you have a 1 Ranged, a 2 Ranged and a +3 Ranged, and you just need one more damage to trigger Second Chance, you can win. (Resolve 1 Ranged, trigger Second Chance, then resolve the 2 and +3 Ranged.)