Solar battery charger and powerplant
To protect from future edits and to provide a more readable and properly cropped copy, here is the circuit you are asking about:



Your question is what are the specs for Tr1.  However, that's the wrong question.

Look at the overall purpose of the circuit.  It would be better to copy its function than its detailed implementation.  This circuit is a rather convoluted way to generate regulated 5 V from a battery of nominal 3.7 V.  There are easier and simpler ways, and they will have better performance.

First, look at this circuit and try to understand at least its basic operation.  T1 pulses, which drives Tr1.  The positive peaks of these pulses pass thru VD1 to make the output voltage.  VD2 provides course regulation by interfering with the oscillations when the output voltage gets too high.  L1, C4, and C5 are additional passive filters to reduce the ripple on the output.

So again, all this does is take the battery voltage as input, and produce a somewhat regulated 5 V on the output.  Otherwise this is not a great circuit.  My guess is that it was designed to use particular cheap parts in high volume and to be well suited to the production capability of a particular factory.  Some of the parts may also have been chosen because they were already used in volume on other products.

However, none of these benefits pertain to you who just wants to build one on his own.  You are only left with the convoluted, overly-complex, and inefficient design, calling for parts with unknown specs.

What you really want is a plain and simple boost converter.  There are many chips out there that do most of this for you.  Particularly at these low voltages, look at the offerings from Microchip.  You can get parts that contain the switch and control circuitry, maybe even with a synchronous rectifier.  You add the inductor and output caps, the input cap, and a few extra parts.  The result will have much better output regulation, lower ripple, and higher efficiency that the circuit you show.