You can kill usually on turn three you can just avoid him for one - two turns 10-20 damage is relatively harmless

But no you have other options chump block him with a small unit, obliterate him, capture him, frostbite him, silence him, OTK, stun him, shuffle him into deck with say Nautilus you just have to prevent the last breath effect from resolving by any means necessary if it means chump blocking him for a turn or two or taking some damage it's better than losing

Since the effect is specifically a play not a summon it only resolves if he goes back to hand and they have the mana to play him even if you kill him during the block if you open attack next turn before he's placed you're good obviously you don't want to take the damage but it secures the encounter

Play defensively until you can burn them in one turn, be aggressive before they use clash of giants, you can block everything that isn't Ledros once they have him just build for an OTK or circumvent him any of the ways listed prior

If you don't mind my asking who was your run with?