Can you completely kill a big slime with a single detonation of TNT?

Yes. You just need a lot more of it.

I got three or four large ones... Oops.

If the TNT all exploded at the same time, then no. This is because it all hits the big slime and by the time it separates all the TNT is gone. You could use repeaters/redstone torches to have a few delayed TNT explosions. Then there would be only one ignition and it could still kill the slime.

I don't think this is possible. TNT triggering TNT causes a very short ‘fuse’ on the target, so all the TNT near the slime will be quickly gone, and anything distant won't have time to fall down on the slime. Note that a stack of TNT can be triggered from the bottom and will chain all the way to the top without falling away — it's very fast.

I found that I could cause such stacked TNT to fall further before exploding by layering it with stone — the stone above the TNT prevents it from hopping upward when triggered, allowing it to fall down sooner. This was not enough to kill a slime, but I didn't design the structure very thoughtfully.

It is impossible to completely kill a large slime with a single piece of TNT.

This is because slimes have multiple stages to their health, and TNT can only take away one, thus dividing the slime.

As in the photo above with the multiple pieces of TNT, that works because multiple blasts can then kill the smaller slimes after the big slime has been split.