Well Roaming Legendaries are obviously tricky until you get really online with Pokémon and breed a dedicated capture poké / team (in my case it was Baton Pass + Mean Look Umbreon and Technician False Swipe Scizor, now its a Gallade with Hypnosis, Swords Dance, False Swipe, and Mean Look).
But for stationaries, it has to be the Hoenn trio in Emerald (with a shoutout to Lati@s for being incredibly tiresome to reset for, given its triggered the second you leave your bedroom and they can't be tracked until you've randomly encountered them once). The Champion tops out at lv. 58, and its highly unlikely you'll ever have the patience to get to 4+ rematches with Juan and his lv. 66 Kingdra...so most likely your team is high lv. 40s, low lv. 50s at most with no simple way to train them up to face Groudon, Kyogre, Rayquaza and Steven.
So not only are you facing down a 20-level disadvantage, Kyogre and Groudon both have OHKO moves that increase with accuracy the greater the level gap, and they're obviously 600BST Pokémon, and they have a low catch rate. Kyogre in particular has only 35 PP when Timer Balls take 30 turns to get to their most effective, and Drizzle powers up its STAB Hydro Pump even further. Oh, and it can heal itself. Groudon is slightly easier as Fire Blast is off its weaker attack (and not STAB), but it has no-charge SolarBeam and Fire Blast to hit the Water- and Grass-types you would obviously send out against it as well as Rest and 1HKO again, and only 30 PP. Then we get to Rayquaza. No 1HKO move, but it'll either heal itself with Rest or sweep half your team then knock itself out with Outrage (only resisted by Steel-types), and Fly means you can spend 15 turns unable to even attempt capture (although its a good time to heal). Plus the Mach Bike puzzle to get to it is genuinely difficult even as an adult. I think I actually ran out of money the first time I faced Kyogre due to a combo of PokéBall expenditure and dropping money when my team got wiped out.
In fact Hoenn legendaries in general are just a nightmare to face, given you have to solve a route-long puzzle, then Dive, then solve a braille puzzle which requires you to have two specific water-types, then another braille puzzle in order to face them. I prefer it to how in the next couple of generations legends all just encountered and battled, like a box-ticking exercise.
Giratina is a tough one in Gen IV too because Shadow Force hits through Protect and its immune to False Swipe.