This is what I've gathered so far in my experience:
Search Level: The higher the search level, the more information the dexnav provides you. It will indicate notable rare moves, held items, IV potentials, hidden abilities, overpowered levels, and national dex Pokemon such as Zorua. You can grind/increase the search level by encountering the species in single battles or horde battles. It is speculated that a higher search level increases your odds at finding a shiny. However, you ought to chain for a shiny Pokemon.
Chaining: This will increase your chances of finding a rare or good IV Pokemon. Use repel and then Search for any caught species using the dexnav.
- When chaining, you must either KO or capture the Pokemon. Do not flee.
- Click Search again immediately after the battle ends and remain still until dexnav Finds something. Then, Sneak to that next Pokemon.
- If you'd like to walk around cautiously, then... you may Sneak to other triggered shaking spots. If you simply encounter a wild Pokemon (i.e. you're not using your repels), the encounter can break the chain.
- When dexnav cannot Find any more Pokemon, you may either Search for a different species or walk around a bit until a shaking spot naturally triggers. Sneak up to that new shaking spot and continue the chain, regardless of its species.
- You may Search for a different species and not break the chain. You can begin the chain with one species and then transition to some other species as long as it is a Sneak.
- Do not leave the route.
- If you want to take a break, put your 3DS in sleep mode while in a battle rather than standing around.
- Do not use the itemfinder nor the bicycle in the area. If you activate these items near a shaking spot, the Pokemon may run away.
- Avoid running. If you run around and a shaking spot naturally triggers, you risk scaring away the Pokemon and breaking the chain. Run several tiles away from grassy areas if you need to "recharge" the dexnav if it won't Find anything.
- Roaming trainers that literally run into the shaking spot will scare away the Pokemon and break your chain.
- Trading does not break your chain. I tested this myself.
- Basically, search level is unique to the particular species (i.e. Swablu), but the chain increases for every successful Dexnav Sneak (I rotated between some 3 Pokemon on a route and my chain continued).
You will find that your chain is successfully continuing as the wild Pokemon's level rises. Every 5th consecutive battle has a Pokemon with a very high level compared to the route. After every set of 5, the other Pokemon's base levels rise by 1 level. For example, I encountered these on route 114 with the Swablu and Seviper/Zangoose:
1st to 4th battles: Level 19
5th battle:
Level 29
6th to 9th battles: Level 20
10th battle:
Level 30
11th to 14th battles: Level 21
15th battle:
Level 31
16th to 19th battles: Level 22
20th battle:
Level 32
21st to 24th battles: Level 23
25th battle:
Level 33
and so on.
Obviously, the level may climb as well as into the 60s. At some point, the dexnav resets the level of the wild Pokemon to prevent this. Your chain still continues.
More information here.
