Intra-Venus Inc is the largest company in the known universe. It's Chairman and president, Josiah W Dogbolter, has called a special shareholders meeting. He tells them that the Time Lords of Gallifrey have monopolised time for long enough. He intends to open the corridors of time for private enterprise (for the benefit of everyone). With a flourish he displays the means to do this: the Dogbolter Temporal Rocket. It will allow individuals to attend any period in history that they wish.
After the meeting he turns to his robot assistant, Hob, and asks how the presentation went. Hob is positive with the proviso that the temporal rocket has never actually been tested. Undeterred, Dogbolter says that he has a plan to test the rocket. He is going to find a spectacularly stupid assassin, strap him to the rocket and send him after the Doctor. Hob says he knows the ideal assassin, one who already has a grudge against the Doctor, and makes his way to Death's Head's room with a letter of introduction.
Death's Head is impressed; the letter is written on paper - a fantastically expensive material. Hob points out that he is the most expensive robot ever made: jewels, platinum and gold leaf are his constituent materials. He adds that he will belong to Death's Head if the assassination is completed satisfactorily. Death's Head looks at the letter and the enclosed pictures of the fifth, sixth and seventh Doctors. He agrees to take the job.
Several days later, at Intra-Venus HQ, Death's Head completes some rudimentary training on the Temporal Rocket and launches himself. He briefly appears in the small village of Thetford in 1646 (close enough to a Mistress Thorogood to have her condemned to the gallows) and then again in the Triassic period (leaving footprints that would baffle geologists millions of years later) and once more in the Battle of the Somme (where he mistakes a tank for his mother).
Finally he arrives on the stage of an end-of-the-pier show where the Doctor is appearing as the Fool in a pantomime. He unleashes a shot from his blaster that misses the Doctor but sets the theatre on fire. The Doctor uses the pandemonium that ensues to get into a pantomime horse with a friend and sneak out of the theatre. He gets out of the costume and makes his way to an amusement arcade where the TARDIS is waiting. He is just about to set the coordinates to a random destination when Death's Head bursts into the control room. An alarm begins to sound and the Doctor tells the assassin that he has a thermo-nuclear device strapped to his back. Death's Head immediately suspects Dogbolter of double-cross. The Doctor adds that they are being scanned by a powerful device, possible a detonating beam.
Death's Head can't release the clamps holding the device to his back so he orders the Doctor to follow the beam back to its source. The TARDIS lands on the roof of Intra-Venus HQ. Dogbolter's first instinct is to head up to the roof but Hob persuades him to go down to the sub-basement (which is lined with lead). Meanwhile, in the TARDIS, Death's Head gives the Doctor his gun and tells him to blast the device off his back. The Doctor tries but fails. The Doctor produces his own invention, a piklok, and unfastens the clasp.
Dogbolter and Hob hit a problem when their elevator demands security clearance to proceed to the sub-basement. Hob finds it in Dogbolter's pocket. Death's Head throws the bomb out of the TARDIS and he and the Doctor dematerialise just as it explodes. They reappear on top of a tall building in another city. Death's Head exits the TARDIS, telling the Doctor that they are quits for now. The Doctor says that it won't be easy to kill him, especially for a creature like Death's Head who doesn't know how to change. He says that a machine like Death's Head cannot grow organically. The assassin replies that what the Doctor is describing isn't change, it's just 'falling apart.'
As the TARDIS dematerialises Death's Head surveys the city around him and realises that he doesn't know where he is.