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I used Spell Focus and some other base spells with low cooldown (Gem Resonance, Ritual Of Power), high spell shards recovery and Spellhound to get it. Don't forget to put 75 points into Empathy for extra 50% pet experience bonus.
That really seems like a bad idea to use apprentice.
1e126 mysteries, if that's any help.
I did it long before I had any items that increase exp, so no Falconer bonuses. If you are lucky and got some of those items, sure, they help a lot. I only used bonus from 75 in Empathy and put remaining attributes in Wisdom.
I don't see why Shadow Stalker would be a better option - its experience gains according to wiki: (2*K+F)*M, where K=5 if not idle, 1 if idle, F - fixed pet experience bonus, M - pet experience multiplier. If you have 25 in empathy, then F will be at least 100, so bonus from keeping mode not idle becomes less important. I think demonologist has some upgrades that further increase F value. Spellhound exp gains are (0.8 × S + F) × M, where F and M are the same as before and S is spellshard cost of spells that you cast.
As long as you can cast spells with 2*5/0.8=12.5 worth of spellshards per second Spellhound will be better than Shadow Stalker.
Spell Focus costs 22 spells shards and with attributes focused on Wisdom you gain at least 88 shards from casting it per second (maybe zero sometimes if passive recovery feeds another spell, but with high wisdom they should be at full charges the next second after they were cast, so at least 4 out of 5 seconds all passive shards will be dumped into Spell Focus, so let's use 70 shards per second from Spell Focus for out calculations), it feeds Gem Resonance and Ritual of Power that will be cast as soon as they are off cooldown so that adds 144 from Gem Resonance (720/5) and 495 from Ritual of Power (4950/10). So 10 vs 567 (709*0.8), yeah, it looks like Spellhound is much better with just three of these spells but there are three more slots available that you can also use somehow. Plus if you don't keep idle mode off, then Shadow Stalker's extra experience bonus drop to 2. This calculation didn't include extra spell cost discounts that may have been due to upgrades (I tried to include discount from wisdom 25), it does not include extra Spellhound shard gains, but they are small because most spells are full anyway.
If you include fixed pet experience bonus it becomes something like 210 vs 767 (I used F=200 because I don't remember the actual one, but it should be 100 from 25 empathy + some more from upgrades that I don't think will be more than another 100) so not such a huge difference anymore, but still Shadow Stalker seems to be 3 times slower.
I don't remember how much time it took or how many mysteries I had, it was just a minor achievement that I got without much trouble. Compared to Dwarven preparation+Tranquility which took a run that lasted 4 days 22 hours at e202 mysteries it was nothing.
If you use items for this secret achievement, you're doing it way too late.
Spellhound and Pixie are the two fastest leveling pet in normal circumstances.