Lugia
Lugia is a combination Psychic/Flying Pokemon, obtainable only by winning the Silver Feather after you defeat Team Rocket and the Kimono Girls. Lugia is located at Whirl Islands. You must also be at least level 45 to have a chance at catching Lugia, making her a late-game Pokemon. Lugia, along with Ho-Oh, MewTwo and others, is a Legendary Pokemon with particularly powerful attacks. These include Rain Dance and AeroBlast. Capture Lugia with a Great Ball.
Ho-Oh
Ho-Oh is a Phoenix Pokemon who uses fire-based attacks. These are among the most powerful elemental attacks in ̶0;SoulSilver.̶1; Ho-Oh is only obtainable once you have won the Rainbow Wing. You must defeat Team Rocket and the Kimono Girls to win the Rainbow Wing. Take the Rainbow Wing to the Bell Tower. Ho-Oh is at the top. He is level 70 and difficult to capture. Use your Master Ball to do so. Like Lugia, Ho-Oh is a Legendary Pokemon.
Mewtwo
Mewtwo is a powerful Legendary Pokemon of the Psychic type. To obtain Mewtwo, you must first earn all badges that can be won in the Kanto region of the game. This gives you access to the Cerulean Cave, at the end of which is Mewtwo. Like Ho-Oh, Mewtwo is level 70, so you will need other powerful Pokemon to obtain him. He has some of the most powerful Psychic attacks in the game, including Amnesia and Psycho Cut.
Other Strong Pokemon in "SoulSilver"
The Legendary Pokemon as a group are the most powerful in the game, but some regular Pokemon rival them when fully developed. Arceus is one such Pokemon, but he is notoriously difficult to catch. Giratina is a Legendary Pokemon with particularly powerful Dragon attacks. Darkrai is among the most powerful Dark type Pokemon, and uses Bad Dreams, a move that may be the most powerful Dark attack.