Chachapoyas is not easy to reach, which is part of what keeps it uncrowded.
By bus from Chiclayo: The most common approach — an 8–10-hour journey on winding Andean roads, with several companies running overnight services. The road is paved and reasonably good; the scenery through the western Andes and into the cloud forest is spectacular.
By air: The nearest airport is Chachapoyas Airport (CHH), with small propeller aircraft connecting to Lima via Jaén or Tarapoto. Schedules are limited and weather-dependent. A more reliable option is to fly to Chiclayo (CFG) — well served by Lima flights — and take the bus from there.
From Tarapoto: An alternative entry from the east — a roughly 8-hour drive through Amazon lowland and up into the cloud forest. Less common but scenic in a different way.
The bus journey from Chiclayo at night means arriving in Chachapoyas at dawn, which works well — you can sleep on the bus and wake up in the mountains.