In Pokemon sword I'm trying to catch the galarian legendary birds, they break out of ultra balls in one shake even with a sliver of health.
You aren't unlucky. The legendary Galarian Birds have a catch rate of 3, which means they have a chance of 1.6% getting caught at full HP through a Pokeball. Read this post to find out which Pokeball works the best. The best way is to bring a Pokemon with False Swipe to ensure they are at 1 HP, then give it status condition. Sleep and Paralysis are your best bet, Freezing is rare plus not recommended since only you can have the condition through damaging ice-types moves. Poison and Burn are very bad; they slowly take its HP away which means you have a set time to catch them, that is very risky.
