Item Requirement
The item required for Poliwrath to evolve is the Water Stone --- the same item used to evolve Cloyster, Starmie, Vaporeon, Ludicolo and Simipour. (A secondary use of this item is to open one of the doors in the Ruins of Alph.) The item used to get Politoed --- the other final evolution for the Poliwag family --- is the King's Rock. Part of the requirements for getting Politoed is equipping Poliwhirl with the King's Rock. If you never equip it with this item, you will not risk becoming unable to evolve it into Poliwrath.
Finding a Water Stone
There are a few different ways to find a Water Stone in "Pokemon SoulSilver." Bill's Grandfather, who lives next to the gym in Fuchsia City, will give you one if you have a Staryu or Marill when you talk to him. You can also purchase Water Stones from the Athlete Shop in the Pokeathlon Dome for 2,500 athlete points on Monday, Tuesday, Wednesday or Friday. Additionally, first prize for winning the bug-catching contest in Johto's national park is sometimes a Water Stone. However, this is a randomly chosen reward.
Evolving Poliwrath
Poliwrath evolves when you use the Water Stone on Poliwhirl, the second evolution of Poliwag. (Poliwag cannot directly evolve into Poliwrath.) Poliwag evolves into Poliwhirl at level 25; there are no level or trading conditions required for this evolution to occur. However, although you can evolve Poliwrath at level 25, doing so is not necessarily a good strategy. Poliwrath does not learn any additional moves until he reaches level 43, whereas Poliwhirl learns Bubble Beam, Mud Shot and Belly Drum between levels 25 and 43. However, you can circumvent this issue by using technical machine (TM) or hidden machine (HM) items to teach Poliwrath new moves instead of learning moves by leveling up.
Additional Methods of Acquiring Poliwrath
The only way to acquire Poliwrath in "Pokemon SoulSilver" is by evolving Poliwhirl into Poliwrath using the Water Stone. Poliwhirl does not appear as a wild Pokemon, so it is not possible to catch Poliwrath. It is possible to get Poliwrath by trading with another player, however. The method for getting Poliwrath is identical in almost every version of "Pokemon," with the exceptions of "Pokemon White" and "Pokemon Black," in which you may catch Poliwrath in the wild. Trading with a player who has one of these two versions of "Pokemon" is the only way to get Poliwrath in "Pokemon SoulSilver" without evolving him using a Water Stone.