Egg Moves are moves that a Pokemon can usually only learn via breeding. Or, they can learn it via level up or TM, but they can also get it from breeding as well for convenience.
(Those challenging the Little Cup , which uses base evolution Pokemon at level 5, will rely heavily on Egg Moves to get Little Cup Pokemon with formidable movesets.)
Both males and females can pass on Egg Moves, but since Egg Moves usually come from Pokemon of a different species, males are the most valuable for this, and females are used to chain breed if trying to get multiple Egg Moves on one offspring.
Example using Totodile
Let’s use an example (note, this example assumes Sun and Moon only with no access to Pokemon Bank). This will demonstrate Chain Breeding as well. Totodile (available through Island Scan) can learn Aqua Jet and Dragon Dance both as Egg Moves.
Both are excellent moves, but both moves are also learned via level up in Sun and Moon by different potential parents. Let’s start with the first one, Aqua Jet. Popplio learns this via level up and is in the same Egg Group as Totodile.
Level up Popplio until it learns Aqua Jet or go to the Move Reminder, who can now teach a Pokemon any level up move it learns regardless of its actual level. Breed a male Popplio with a female Totodile. The offspring will now know Aqua Jet!
Now, the last move is Dragon Dance . Because Dratini is in both Dragon and Water 1 Egg Groups, it is the ideal father for a female Totodile that knows Aqua Jet.
Level up Dratini until it learns Dragon Dance or teach via the Move Reminder, and breed a male Dratini with a female Totodile that already knows Aqua Jet and you’ll now have a Totodile with Dragon Dance and Aqua Jet!
Other moves, such as Gible and Outrage, and Extreme Speed and Dratini, are extremely valuable but are only learned through Egg Moves.
As you breed Egg Moves, if you don’t want to lose a nature you’ve already gotten, just equip the female carrying the Egg Moves with the Everstone. Everstone will not impede on the ability for Egg Moves to be passed down to offspring. You’ll get two things done at once!
Also, you don’t have to worry about RNG here. Egg Moves, if done right, have a 100% chance of being passed down.
Smeargle is a Pokemon you can catch fairly early on (Route 2) and is an excellent breeding assist in the Egg Group it’s found in.
Field Egg Group is the largest Egg Group, with Pokemon as varied as Skitty and Wailord both belonging there. Any Pokemon in the Field Egg Group can thus benefit greatly from Smeargle when it comes to transferring Egg Moves.
The reason is because Smeargle can learn Sketch , its signature move. Sketch only has 1 PP but using it after the target Pokemon uses a move makes Smeargle learn that move. Yes, Smeargle can learn any move! (Well, except Darkrai’s Dark Void.)
This means any Pokemon in the Field Egg Group can learn any combination of Egg Moves without needing to chain breed.
Unfortunately, in these games there is currently no way to purposefully trigger a Double Battle so that you can have Smeargle Sketch your own other ally. Instead, you’re going to have to use a bunch of wild Smeargle.
First, you will obviously need a Smeargle, so go to Route 2 and catch one. Chances are, you’ll need to use False Swipe to catch it. It would also help a lot if you used Thunder Wave–not only will this make it easier to catch, but it’ll stop it calling for help.
After catching your Smeargle, train it a little, ideally until it learns Sketch again (assuming it no longer has it, which is likely). Smeargle learns Sketch at level 11, 22, 33, and so on, so it should be easy. Alternatively, you can just go back to the Move Reminder and learn Sketch again.
Next, make your way back to Route 2 and find another wild Smeargle. Make sure to lead with the Pokemon whose move you want to sketch, with your Smeargle waiting at the back.
If you want to sketch a status move or a very weak offensive move, immediately use it on the wild Smeargle. After the wild Smeargle sketches the move, switch in your own Smeargle and sketch the move from the wild Smeargle.
However if you want to sketch a stronger offensive move, instead use an Adrenaline Orb on your first turn and patiently wait for the wild Smeargle to call for another wild Smeargle.
Doing this will have the side effect of causing the first Smeargle to fail to sketch anything, making it use Struggle for the remaining turns. After 4 Struggles, it will faint, so hopefully it will successively summon a Smeargle by then.
If another Smeargle doesn’t appear, just keep using an Adrenaline Orb. This will have absolutely zero effect, but you won’t consume an Adrenaline Orb on subsequent turns, which is an easy way to "waste" turns.
Once there are two Smeargles on the field, use your offensive move to KO the initial Smeargle. The freshly-summoned Smeargle that’s still around will sketch your move. Now switch in your own Smeargle and sketch this move.
At this stage, it’s important that your own Smeargle is strong enough to survive the other Smeargle’s moves!
Afterwards, you can repeat the process until you’ve filled your Smeargle out with the Egg Moves you want.
Note that moves that hit the whole area are much more difficult to Sketch, but thankfully the big ones like Surf and Earthquake are TMs.
A Smeargle for Thoughts?
Because of Smeargle’s versatility, you can (and maybe should) make a Smeargle for SOS Chaining too. Having a Smeargle know False Swipe, a move that can KO Pokemon but with lots of PP, and Spore or another status move can make it an all-purpose SOS Chaining and catching too.
That way, you don’t have to constantly switch Pokemon. And if you need to trigger a weather-specific SOS, the fourth slot can be Rain Dance, Sunny Day, Sandstorm, or Hail. Make sure you equip Safety Goggles to Smeargle if triggering the last two weather conditions so you don’t take chip damage.
You’ll also want to make sure the Smeargle is at a very high level.