Desert-to-Adriatic routings rarely reward patience the way Tucson to Zagreb does, and after years of booking this itinerary for clients and myself, I can say definitively: there is no nonstop option, so business class from Tucson to Zagreb always routes through at least one major hub, with Frankfurt, Amsterdam-adjacent Atlanta connections, or Munich proving the most reliable gateways depending on whether you lean toward Delta's SkyTeam network or Lufthansa's own metal. The total journey, door to door, typically runs well beyond the 11.5-hour air time once you factor in the TUS-to-hub segment, so I always advise treating this as a two-day travel event rather than a single overnight sprint.
My preferred build is Delta out of Tucson connecting through Atlanta or Detroit into a transatlantic partner, then finishing on Croatia Airlines (OU) metal from a European hub into Zagreb — OU doesn't operate widebody business cabins, so their intra-European business class is more about seat blocking and lounge access than a lie-flat product, and savvy travelers shouldn't expect Qsuite-level hardware on that final hop. Where the real comfort investment pays off is the long-haul segment: if your itinerary routes through Frankfurt or Munich, seek out Lufthansa's Allegris business class where it's been deployed on the relevant aircraft, since the redesigned suites with adjustable panels are a meaningful step up from the airline's older long-haul product. My insider tip: when booking through Munich, build in a minimum 2-hour connection specifically to use the Lufthansa business lounge showers before the short Zagreb hop — arriving in Croatia refreshed rather than rumpled matters when Zagreb's compact airport offers little in the way of arrival amenities.
January through March and again in October and November consistently show the softest business class pricing on this corridor, as Croatian tourism demand collapses outside summer while airline capacity holds steady. Given how thinly scheduled and fare-volatile this routing is, I'd strongly encourage setting up automated fare alerts rather than manually checking, since favorable business class pricing here tends to appear briefly and without much warning.