Chaining... Shooting Star Dragon

SS Shooting Star Dragon. Opponent uses Bottomless.. activate eff.. Opponent uses Torrential Tribute..

How does that play out? Does Torrential miss it's timing? Or does it work and everything get destroyed?

Torrential Tribute will destroy everything. Bottomless is Link 1, Shooting Link 2 and TT Link 3. The reason it will not miss the timing is that there are two windows for activating cards when a monster is summoned: the negation window and the response window. The negation window means the monster is basically just waiting to see if it's ok to hit the field, waiting for Solemn Warning/Judgment and such cards. The response window means the monster is on the field and he can contribute to that window himself. Bottomless and TT both activate in the second window. BTH activates first, then Shooting negates it, then TT can be legally activated.

that "response to the summon" window includes the whole chain that is activated in response to that summon. For example it would be perfectly legal to activate anything as the first 3 chain links and then activate bottomless as link 4.
Just think of it, without that a chain to a trigger like caius with bottomless wouldn't be possible. Yet, you do that quite often