You are cutting it too close in the afternoon. Here's why- based on my experience:
You will park in the central area near the visitor center and will have to either Walk uphill (45 minutes) or take the shuttle bus (small fee) (or take the horse drawn carriage) Allow 15-30 minutes depending on when you catch the shuttle.
The shuttle will drop you off ABOVE N-Stein. And the path to St. Mary's bridge starts here also.
You should allot time to walk to St Mary's bridge from here before your visit to N-Stein or you will be walking back up hill after your visit.
Although, it may be a 10-15 minute walk downhill to the entrance, it will be a 20-30 minute walk back up the hill.
If you disregard my advice to visit St Mary's bridge first, OK, fine
You will then walk downhill about 10-15 minutes to the entrance gates.
You will will want to be at the entrance gates about 15 minutes before your ticket time.
At that time, you will be allowed into the castle waiting area. At your designated ticket time, the electronic gates will open and allow ticket holder inside and you find your tour guide.
I think it's about an hour tour, but we lingered after the tour to get pictures and see exhibits.
So 9:55 am entrance means you could be done by 11:15am.
If you now want to walk 20-30 minutes back up the steep path to St Mary's bridge, and allot another 30 minutes at the bridge.
Then you have to walk back down to visitor center on the same path you took up. Allow a bare minimum of 30-45 minutes to walk for that. Or you could run. Or hope the shuttle was at the top of the hill when you needed it.
Once down at the visitors center, it is a 30 minute leisurely walk up the road to Hohenschwangau.
So you won't make a 12:25 tour unless you are running the entire way.
And when are you going to eat lunch? Use the rest room?
Here's what we did: 10:50 tickets to N-stein, 2 Pm tickets to Hohenschwangau
Arrived at 9:15am and parked. Caught the 9:45 shuttle up. Arrived at drop off point at 10. Walked out to the bridge for 20- 30 minutes. Then walked down to castle entrance 10-15 minutes. Entered the castle 5-10 minutes before ticket time.
Tour was about an hour and a half.
Afterward, walked down the hill from N-Stein, 30-45 minute walk.
Had lunch 30-45 minutes. If the restaurant are crowded, it will take longer.
At 1:15 pm, began our leisurely walk up the road to Hohen.... Arrived at 1:45 pm. Tour began at 2 pm.
Done by 3 pm. Walk back down to parking lot/visitor center.
Timing is approximate, but you get the idea, I hope.