(Kyokujitsu shouten no ikioi; “[with] the force of the rising sun”)
Vigorous, energetic, and forceful like the sun rising in the morning sky toward its zenith.
旭 by itself can be read asahi, “morning sun.” 旭日 (kyokujitsu) is simply adding “sun,” so “morning sun” or “rising sun” is still an appropriate translation. 昇 (here read as shou) is “to ascend” and 天 (ten) is still “the sky” or “the heavens,” so 昇天 (shouten) in this context means “rising up the sky.”
All the above acts together as a single noun phrase, and associated with it by the particle の (no) is another noun, 勢い (ikioi), “force,” “energy,” “authority,” “momentum,” etc.
Incidentally, there’s a medal that the Japanese government awards to distinguished individuals, generally for international-relations or cultural achievements called the “Order of the Rising Sun” – the 旭日賞 (kyokujitsu shou). Well, it’s hardly a coincidence that the late Meiji-era government of the “land of the rising sun” created a medal promoting an association between the rising sun and boundless, triumphant energy.
The initial four charactes can be detached from the rest of the phrase and used yojijukugo style.
(This time from a dictionary; things have been rather hectic and coming up with a satisfying – and grammatically correct – example of usage on my own can be the most time-consuming part of one of these posts!)
(“Kyokujitsushouten no ikioi de kachitsudzuke, kesshousen ni nozomu.”)
[“After winning a string of victories with overwhelming force, they looked forward to the final match of the tournament.”]