THE HOUSE OF THE DEAD: Remake

For the Normal and Third endings that require you to score below 62,000 points, use Classic scoring. In all of my playthroughs with Classic scoring, I never even came close to 62,000 points, so you don't have to worry about scoring too much. My best run was around 46,000 points.

As for the last score digit being either a zero (for this achievement) or a five (for Normal ending (20G)), there is actually a really easy way to guarantee you beat the game with the score you want to get the proper ending. For that, it's important to realize that any enemy you kill will give you a score with a five on the end (for example, 85 for a regular kill or 205 for a headshot/heavy kill), and any boss you kill with give you a score with a zero on the end. This is all for Classic scoring only, of course. Therefore, enemies as the only way to vary your score. So, play like normal up until Chapter 4, the final chapter, killing enemies and getting whatever score. It doesn't matter at all. 

In Chapter 4 is where you can control your score to get the ending you want. Here is what Chapter 4 consists of:
 

1. Two pairs of enemies
2. Refight of the first boss
3. Refight of the second boss
4. Five or six pairs of enemies
5. Fight against the final boss

Since the enemies that you fight are in pairs, their 5s in their scores will cancel out, meaning the digit at the end of your score won't change. Likewise, the bosses' scores give you a number with a zero, so they won't cause your score digit to change. The only thing that will cause your score digit to change is the number of bats you kill during the refight against the second boss. Each bat you kill gives you 15 points. This is how you can make your score end with whatever you want. If you want your score to end in zero and it already does, kill no bats (or an even number of bats). If you need to change your score (either to a five or to a zero), then kill one bat (or an odd number of bats). Purposely wait until there are no bats near the boss's weak spot so you can safely shoot it without killing the wrong number of bats. As long as you have a five or a zero in your score after the second boss fight, that's what your score will end with at the end of the chapter.

If you mess up the second boss fight, you can just pause and quit to the main menu, then Continue your campaign to start the fourth chapter over again and retry, avoiding the need for a whole new playthrough.

As a side note, you can NOT just play through the final chapter to get these achievements. You'll see the appropriate ending but the achievements won't unlock. You need to play through the whole game from start to finish.