Getting the Possessed Ending by itself is fairly trivial, but the caveat for a 10-star rank is that you need under 500 damage points. You also cannot use the unlimited sub-machine gun or the flamethrower as that will deduct a star.
To get the Possessed Ending, you need at least 4000 hit points. Forgiving the woman in the confession booth gives you 1000 for free, so you need to get the remaining 3000 during your playthrough. If you maintain your damage points as close to 500 as possible, that means you need to defeat more than 250 enemies for over 2500 hit points (250 x 10 = 2500). I think the game does give you more than 250 enemies to defeat on Hard difficulty or above, but barely.
Technically, the Infinite Monster Respawn exploit can be used to fill in the numbers, but I'm trying to see if it can be done without relying on this exploit.
EDIT:
First run. Extreme X w/ bullet adjust x5 (no infinite submachine gun or flamethrower). No infinite monster respawn.
Total hit point: 4341
Overshot total damage by: 562 (1061 minus 499)
Under-achieved defeat count: 23 (251 minus 228)
251 kills and 490 damage points would have given me exactly 4000 hit points.
Each additional kill allows you to deduct 10 damage points and achieve 4000 hit points.
So, I think it's possible to get Possessed Ending and 10-star rank at the same time. I'm going back to see which monsters I need to defeat to fill in the 23. It's mostly rooms with two or more Pendulums and the one room where four Closers spawn in the Church.
Ending type: Possessed
Action Level: Extreme X (5/5 stars)
Riddle Level: Hard (5/5 stars)
Clear time: 2h 51m 56s (10/10 stars)
Split worm kill time: 1m 20s (2/2 stars)
Missionary kill time: 1m 35s (2/2 stars)
Leonard kill time: 1m 42s (2/2 stars)
Memory of Alessa kill time: 1m 44s (2/2 stars)
The god kill time: 5m 06s (2/2 stars)
Clear number: 32 (5/5 stars)
Save & continue number: 28 (1/5 stars)
Item number: 135 (20/20 stars)
Extra weapon number: 5 (5/5 stars)
Defeated enemy by shooting: 155 (15/15 stars)
Defeated enemy by fighting: 73 (14/15 stars)
Total damage: 1061 (3/5 stars)
RANK: 93/100 stars (9 big stars, 3 little stars)