Quick checklist:
1. Make sure you actually have all of the required spells for each category.
Pyromancy:
Miracle:
Sorcery:
2. So, if you do have everything, then we can confirm that the API (basically the thing that records your achievement progress) did not update when you collected a certain spell. The leading causes for this involve playing offline or XBL being down while you collected a certain spell.
3. Replay the game on your current character (you will likely be doing this anyway while trying to get Knight's Honor, which requires 2.25 playthrus in order to get every weapon). During this time, seek out the spawn areas for each spell from the set that you missed. See the above links in 1. for your missing spell sets. This is to ensure that your API had updated for each of the spells that can show up on each playthru.
4. If that didn't work, there is literally only 1 other option: make a new character. Unfortunately, the API did not update during the time you grabbed a spell that only spawns once per character.
For Pyromancy: This just means you have to rush down to BlightTown, kill Quelaag and meet best girl (Quelaag's Sister). Join the covenant and offer 30 humanities (just dupe a Firekeeper Soul 6 times) in order to get these 2 exclusive pyromancies. Your achievement should pop after receiving 1 or both Great Chaos Fireball and Chaos Storm.
For Miracle: *sigh* You need to do 3 different covenant lines unfortunately. Start with the most likely suspect of the 3 (ie. the covenant where you are likely certain that you received rewards for while offline). There are 6 miracles given as covenant rewards:
Gravelord Sword Dance: join the Gravelord Servant covenant
Gravelord Greatsword Dance: offer 10 Eye of Death to the Gravelord Servant covenant
Darkmoon Blade: offer 10 Souvenir of Reprisal to the Darkmoon Blade covenant
Lightning Spear: Join the Warrior of Sunlight covenant
Great Lightning Spear: offer 10 Sunlight Medals to the Warrior of Sunlight covenant
Sunlight Spear: offer the Soul of Gwyn to the Warrior of Sunlight covenant
For Sorcery: While there are no covenant rewards that come to mind, the Big Hat Logan questline can be glitchy for some so I would recommend revisiting this.
With all of that, you should be able to unlock all 3. Just remember to stay online. Tested on 3 separate accounts.