1.
144 Articuno World Axel Underground 2F Ice Area
145 Zapdos World Axel Underground 2F Factory Area
146 Moltres World Axel Underground 1F Magma Area
150 Mewtwo All Factory Areas (After Completion of Battle Royale EX-6)
151 Mew Sunny Seashore Factory Area (After meeting 80 people)
243 Raikou World Axel Underground 1F Green Area
244 Entei World Axel Underground 2F Cave Area
245 Suicune World Axel Underground 2F Lake Area
249 Lugia All Beach Areas
250 Ho-Oh Volcanic Slope - Red Area
Firebreathing Mountain - Red Area
251 Celebi Everspring Valley Forest Area (After meeting 80 people)
377 Regirock Sunny Seashore Rock Area
378 Regice Frozen Tundra Ice Area
379 Registeel Sunny Seashore Factory Area
380 Latias All Green Areas
381 Latios All Green Areas
382 Kyogre All Beach Areas
383 Groudon All Magma Areas
384 Rayquaza All Tower Areas
385 Jirachi Firebreathing Mountain Tower area (After meeting 40 people)
386 Deoxys All Factory Areas
386 Deoxys All Factory Areas
386 Deoxys All Factory Areas
386 Deoxys All Factory Areas
480 Uxie Sun-Dappled Bank Lake Area (After meeting 2 people)
481 Mesprit Soothing Shore Lake Area (After meeting 5 people)
482 Azelf Shimmering Lake Lake Area (After meeting 10 people)
483 Dialga All Cave Areas
484 Palkia All Lake Areas
485 Heatran All Magma Areas
486 Regigigas All Desert Areas
487 Giratina All Horror Areas
488 Cresselia All Field Areas
489 Phione Rugged Flats Beach Area (After meeting 20 people)
490 Manaphy Rugged Flats Beach Area (After meeting 20 people)
491 Darkrai All Horror Areas
492 Shaymin World Axel Underground 2F Ice Area (After meeting 100 people)
492 Shaymin-S World Axel Underground 1F Forest Area (After meeting 120 people)
493 Arceus All Tower Areas (After Completion of Battle Royale EX-6
494 Victini Beginning Garden
World Axel Underground 2F Tower Area (After meeting 150 people)
638 Cobalion After defeating Terrakion and Virizion
639 Terrakion All Field Areas
640 Virizion All Forest Areas
641 Tornadus Volcanic Slope - Red Area (Requires 3 encounters before battle)
642 Thundurus Firebreathing Mountain - Red Area (Requires 3 encounters before battle)
643 Reshiram All Cave Areas
644 Zekrom All Cave Areas
645 Landorus Volcanic Slope - Red Area (After defeating Tornadus and Thundurus)
646 Kyurem All Ice Areas
Once you've cleared certain areas of the game and return, there is a small chance that you'll encounter Legendary Pokemon. Encountering one will start a boss fight. You'll need to defeat them to proceed with the game and attempt to obtain the Legendary Pokemon. When encountered, Legendary Pokemon take the place of the levels Boss Pokemon. All Legendary Pokemon, however, require you to have finished the story before they will appear.
Source
2.
These appearances are very rare, appearing for 5% of the boss battles, and may require numerous visits before it occurs.
Hope I helped! :)
Source 2
