The boss bird is the one enemy in Skyfall that doesn't spawn on the wave clock at all — it runs on its own independent timer, and that separation was the single most important decision in designing it. Everything else about the boss follows from that one choice.
The first boss can appear as early as 20 seconds into a round, and after one is defeated, the next won't show up for another 40–48 seconds — a randomized window rather than a fixed one. If the boss instead spawned at, say, the start of every wave, its 3-hit health bar would reliably stack on top of the wave-transition spawn-rate jump, and the two systems would compound into a single difficulty wall every 15 seconds. Decoupling the timers means a boss encounter sometimes lands in a calm stretch of a wave and sometimes lands right as things are already getting busy — which keeps every run feeling a little different instead of hitting the same choreographed spike at the same second every time.
A boss's health bar isn't fixed at 3 hits for the whole game — it grows with the wave number you're in when it spawns, capped so it never becomes a bullet sponge. A boss that appears in wave 1 or 2 goes down in 3 hits; reach wave 3 or later and its health climbs a notch, up to a maximum of 7 hits deep into a long run. The logic is simple: a 3-hit boss that shows up when you're already fending off Phantom birds and a full spawn rate would feel trivial by comparison, while a boss that's always tanky would feel like a wall the very first time a new player meets one in wave 1. Tying health to wave number means the boss is always roughly as threatening, relative to everything else on screen, no matter when it happens to spawn.
Its point payout scales the same way — a flat 60 points plus 20 for every point of max health, so a wave-1 boss is worth 120 and a beefier late-run boss is worth meaningfully more. Killing a tougher boss should pay better than killing an easy one; giving them identical rewards would make the harder ones purely a tax on your remaining lives, not a target worth prioritizing.
One more small thing that matters more than it should: a defeated boss triggers the strongest screen shake in the game and a distinct "down" chime, separate from the normal hit sound. That's intentional escalation — every other feedback cue in Skyfall (hit, miss, combo, power-up) is calibrated to be quick and light so it doesn't slow down fast play, but a boss kill is meant to feel like the biggest single moment in a round, so it gets the biggest response.