Be Kind, Rewind

Alternate Future Daily Quest Line - [item=169114]
Start Adapt, Improve, Overcome!.
Then The Final Act follow up.
They you have to kill [npc=154225] to get last Quest Be Kind, Rewind from [npc=153982] (You need craft [item=167062] before entering alternate future).

Almost all the answers here are misleading/incomplete and really annoying since I wasted a vaulbot key for nothing.

First you have to get this quest (which almost all of these answers ignore).
1) So kill the [npc=154225]. If you don't know how to find and kill him go check out his page. It's not trivial. You can't find him when the Chromie alternate timeline quest is up.
2) Talk to Izira to get this quest (immediately after killing Rusty Prince, in the timeline you killed him in).

Ok, now you have the quest and you have two ways to kill Vaultbot:
1) Look for him in the alternate timeline, there you need to use the [item=167062] (you cannot kill him in alternate timeline by kiting).
2) Look for him in normal timeline and there you can kite or you can use the key.

(You can get to the alternate timeline by using [item=169114] or by talking to Chromie if the quest is up. You'll need at least one of those to kill the Rusty Prince.)

Turn in the quest.

You can only kill the Rusty Prince in the "other place".

On days when Chromie offers the daily quest to go to the "other place",
you cannot kill the Rusty Prince, because he does not spawn on those days.
At least I have never seen him there on those days.

On days when Chromie offers the daily quest to go to the "other place",
you can go there and kill enough robots to eventually get the Pascal blue
prints to create time displacers.

Time displacers will take you to the "other place" regardless of Chromie.

On days when Chromie DOES NOT offer the daily quest to go to the "other place",
(she is not there) you should use the time dispacer to go to the "other place".
On those days, The Rusty Prince spawns as well as the Vaultbot.

The first time you kill the Rusty Prince, it unlocks a quest in the other place.
It is found back in town and is called "Be Kind, Rewind".

Be Kind, Rewind requires 2 things ...

0/1 Visual Holo Sphere obtained from Armored Vaultbot
0/1 Craft an Armored Vaultbot key from Pascal (optional)

The reason that the second part is optional is for more than one reason.

One way is for you to be in the "other place" and partied with another
player who has the Vaultbot key. When they open the Vaultbot, you will
loot the Holo Sphere and if it is your first time, you will get the
Pascal blue prints to make the Vaultbot key.

Another way is if you are in the normal timeline and the Vaultbot spawns
and people kite him to the magnet in Bondo's yard, you can loot him and
get the blue prints to make the key. You can also loot the Holo Spehere.

Notice that in the alternate timeline, the magnet is on fire, I don't think
you can kite the Vaultbot to that magnet. The only way to loot the Vaultbot
in that timeline is with the key, which is way easier than kiting him to
the magnet.

Now. If you were to loot the Vaultbot in the other place BEFORE you accept
the quest "Be Kind, Rewind" which would only be AFTER you killed the Rusty
Prince. Now, you are in a delimma because you cannot loot the Vaultbot
anymore that day. Not to worry, wait an hour or so longer and then go back
to the other place and use a key on the Vaultbot for the Holo Sphere then
come out of the alternate time line to turn in the quest. This time he will
not have a star over him on the minimap, but that's okay ... you know where
he spawns, near Boilburn's cave entrance to the east of the main gate to
Junkwatt Depot.

I hope this information helps you.