Design a Li-Po battery charger with small solar panel and charger controller with embedded MPPT
Sorry, that chip is largely unsuitable for your needs. It is a boost converter i.e. generates an output voltage that is higher than the input supply voltage. Given that your SP ranges between 4.25 volts and 5.65 volts AND you only require a maximum output voltage of 4.2 volts, you should be looking for a buck (rather than boost) controller.

The block diagram below shows the transistors that prove to me it's a boost converter: -