Why would a helicopter climb in a spiral?
A helicopter will achieve its best climb rate at a moderate forward speed. Climbing in a spiral helps to have forward speed in what is essentially a vertical climb.

In a hover all the airflow which is available for lift creation must be generated by the rotation of the main rotor. This means that a small amount of air must be accelerated by a lot. If the helicopter adds forward speed, it can achieve a higher mass flow through the rotor, and now less acceleration is needed to achieve the same lift. This improves the efficiency of lift creation. If the helicopter goes faster than its speed for maximum rate of climb, aerodynamic drag grows too high and reduces efficiency again.

The difference can be dramatic: Below is a plot of the speed versus altitude of a generic helicopter and turboprop plane in comparison to the V-22 tilt rotor. Remember that the available power is roughly proportional to air density, and you can start to see how much more power is available for climbing when the helicopter flies with a moderate forward speed.



Flight envelopes of a generic helicopter, a turboprop plane and the V-22 tiltrotor (picture source). Thanks to @mins for inspiring me to expand the answer a little.