This achievement is deceivingly hard at first. After practice, preparation, and planning, it's actually really easy, and requires barely any time at all.
{This solution does contain spoilers, but if you are interested in completing this achievement, chances are I'm not spoiling anything for you.}
~~ Preparation ~~
First off, Richter is an unlockable character and must be unlocked by exploring/ completing the Inverted Castle, which first must be discovered/ unlocked.
To unlock the Inverted Castle, find the Gold and Silver Rings from two optional bosses (one being the Succubus) on any Alucard playthrough to unlock the lower secret chamber that opens from the clock room. Descend into the room to get a pair of glasses from Maria. During the final boss fight of the normal castle with Richter, these glasses make the orb controlling him visible, giving you the chance for the real ending (and unlocking Richter as a character) by killing the orb instead of him. Without the glasses you would get an unofficial ending and fail at unlocking Richter.
When you reach Richter in Dracula's Lair, equip the glasses Maria bestowed upon you to see the orb hovering behind Richter. Defeat it, and, surprise, the game isn't over. The entrance to the Inverted Castle will appear. And now, Inverted Castle time. Explore as much as possible in both castles for map completion, which is what you're really shooting for here.
To unlock Richter, I believe you have to had mapped 180% of the two castles (preferably completed before your ascent to the final area for certainty) when you defeat Shaft and then Dracula, and when you do, Congrats. You have unlocked Richter as a playable character. Now enter "Richter" as a character name to get started. You are halfway there, kinda...
As Richter, you must practice and utilize his two special movement attacks: the Uppercut/ Upwards Lunge (Down, Up, Jump) and the Shoulder Charge/ Forward Dash [can be used in mid air], which uses the same dash move as Alucard's bat form ((Stick Rotation) Up, Up-Back, Back, Back-Down, Down, Down-Forward, Forward, (A, X or B, -- I forget, sorry)).
The Slide Kick move helps a lot, making him invincible as he passes through an enemy and speeding up the process, but I have no idea what the combination is. It's the only move that is not necessary, but could help you a lot. You can look it up if curious.
Used in conjunction, you can pass through most of the areas in the game quickly, easily, and ideally without harm. If mastered, there are a lot of shortcuts you can take that require multiple uses of the Uppercut and Shoulder Charge, include a handful that REQUIRE them, so you should try to sit around for a few moments familiarizing yourself with the special attacks.
~~ Strategy Time ~~
Saving is key for good insurance, although I did this without dying.
*Video included, but it is not mine.
If you are skilled, and know what you're doing, the execution will be really easy, and might take you 20-40 minutes max. Enjoy.
This is almost exactly how I did it myself, but feel free to vary:
At the start, head directly towards Gaibon and Slogra, assuming you know your way around handily. Remember your special moves to get around efficiently. Defeat the infamous duo, and use your Uppercut to reach the top-right most part of their room: I believe there is an area full of sub-weapons to choose from. If not, sorry, I did this all a while ago, but don't worry. If they are in there, you want the *Holy Water*, this will decimate everything in the game if you are in trouble. If I was wrong about the room, you can also get one on the way to the Chapel. A random wall candle in the transition hallway with a magic door to said Chapel should drop one, or just stay stay vigilant, looking for the Holy Water as you run through the game. (The only other one I know of is in the Inverted Castle, in the Clock Area's secret area, directly below Shaft).
Now, you'll want to head towards the Chapel and Bell Tower. You should head to the left and up first to get there, and then start heading up and right, I believe. In these areas, your special moves are key to success and avoiding easy deaths common on the stairs. Just keep moving right and up. I believe you have one boss fight on the way out of the normal castle excluding Gaibon/ Slogra, but your Holy Water should make short work of him (if you must even fight him).
I think you can skip the Clock Tower altogether (a shortcut outside starting from a part of the roof parting from the Chapel/ Bell Towers), going straight to Dracula's Lair, and then taking you to the Inverted Castle.
The Inverted Castle in my opinion was easier opponent-wise because the monsters here seemed stronger but more predictable so as not to overwhelm the player. The shortest, easiest path at some point contains a spiked filled room that requires many uses of your Flying Dash/ Uppercut, which ended up being the hardest room for me to conquer. This room may take major practice and trial and error, so you should want to save before this and be prepared to swallow defeat a few times.
You may have two bosses in your way to the end, depending on which route(s) you take. No problem, Holy water if you have it, otherwise, spam knife rain/ barrage, rinse, wash,... Be careful, a lot of the enemies near the end can be completely over-powered, so watch your step and don't die. The only obstacle worth noting in your way is Shaft now (no Dracula, as Richter already 'killed' him. Sweet). Receive your Holy Water directly below him in the room of sub-Weapons, and Save.
I believe all you have to do is use one Holy Water item smash, and strike him 3-5 times. There is absolutely no challenge in Shaft. Be careful as you fight Shaft though. Although it may be a short fight, he is an over-powered enemy. If luck plays its part, 1st time is a charm and you'll kill him easily.