First you have to beat the game. After that, you go back to fiery field and make it all the way to the top and defeat entei again. If there is enough room in your party, there is a chance that he'll join. To increase these chances, have a friend bow.
Also, Before attacking Entei, throw his favourite gummi at him, (red gummi) you may want to bring 3, as normally they Dodge it. If you do this correctly, he should ask to join your rescue team.
The easiest way to recruit Pokemon is;
-Being level 90-100.
-Having a friend bow
-Throwing their favourite Gummi at them.
-Only have 1 Pokemon ( Or give the other Pokemon a friend bow too )
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No... there is no regigigas in Pokemon Mystery Dungeon Blue Rescue Team. Do you know why? If not... I will tell you. This is because regigigas is one of those new Pokemon from the sinnoh region which was not invented during the time of Pokemon Mystery Dungeon Blue Rescue Team. However, I believe you can find a regigigas in Pokemon Mystery Dungeon Explorers of Time, Darkness, and Sky.
Has to be Blue, In my opinion.
you see every pokemon.
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figure out your self