Before you can play as Richter, you need to have completed one playthrough of the game as Alucard with at least 180% exploration. Once you've done that, start a new game in a new save slot and enter "RICHTER" as the name. This unlocks Richter as a playable character.
After playing with Alucard for so long, Richter can feel like a very different experience. He cannot level up or equip any items or weapons, so there's no experience to be gained or loot to be collected. Fortunately, his default weapon - the whip - is quite powerful and has a very long reach. He, however, is quite weak and cannot sustain much physical damage. In fact, common enemies in the Inverted Castle can kill him in just one or two hits. He also can't double jump, but he can both super jump and chain super jumps to effectively fly across large open spaces, which makes up for the fact that he can't transform into the Bat or Mist.
There are two factors, however, that make the Richter playthrough much faster than playing with Alucard. First of all, since he can't equip items, there's no need to go collect things to advance to new parts of the castle. You can simply walk directly to the teleport room of the Normal Castle, teleport to the Inverted Castle, walk to the Clock Tower, and kill Shaft. Secondly, he's capable of using Item Crashes by pressing . You probably got a taste of this in the Bloodlines stage when you played your first game. The Holy Water Item Crash (Hydrostorm) can kill even bosses in a single use. As long as you farm hearts along the way, you can Hydrostorm everything in the castle to death as you make your way to Shaft.
The shortest route and necessary strategies are nicely laid out in a thread that can be found HERE. Following this, it took me just under an hour to finish the Richter Playthrough from start to finish. That includes time spent farming hearts and a few untimely deaths. Additionally, always use nearby Save Rooms because they will restore your health.