While Peat has amazing stats his low HP makes it important to not get overconfident. Try to avoid unnecessary battles and preserve his HP as much as possible.
On the other hand his low REC allows Peat to take more risks during combat, allowing him to recover quickly from a KO and potentially turn the tables on his opponent. Depending on the situation he could try evading moderately high attack rolls to preserve HP or switch to a more aggressive playstyle when he's behind on stars.
While I'm on Fire! can boost Peat's attack and Rainbow-Colored Circle can help him survive at low HP, battle cards that increase DEF should be avoided as they could be used by his opponents to survive against Blue Crow the Second and are not very helpful for Peat due to his low HP.
Although Scrambled Eve can potentially be used to have Peat end up with 6 or more cards in hand for one turn, using it is a risky gamble as there's no guarantee that he'll draw Blue Crow the Second, while Scrambled Eve could also be used against him to temporarily reduce the cards in his hand to 0 and in the worst case steal his Hyper.
In the same vein attacking Peat while he's at 1 HP will not allow him to use Blue Crow the Second in defense as it would lower his EVD. Be aware of his low REC as if he recovers from his KO quick enough he could potentially use his Hyper in retaliation once he catches up.
Cards like Bad Pudding and Flamethrower can reduce the number of cards in Peat's hand, potentially rendering his Hyper useless.