Let's come to his power and feats.
- Pradyumna killed the all Sons of Sambara in battle.
Krishna's son too, worked up with anger, struck them in the battle each with five arrows shot off his bow. Thereupon those resolute Asuras, exceedingly wroth, set up a net-work of weapons for killing Pradyumna. There at worked up with anger Ananga soon took up his bow .He then killed the ten highly powerful sons of Shamvara.The next moment, filled with anger the powerful son of Keshava soon cut off Chitrasena's head with a Bhalla. There upon the remaining sons of Shamvara, anxious to fight, began to run taking up and discharging arrows. And for killing Ananga they all unitedly fought and shot arrows. The highly powerful son of Krishna, on the other hand, cut off their heads, as if in sport. Having thus slain one hundred sons of Shamvara, all good bow men, he stood in the battle field desirous of fighting.
2. Pradyumna was one of the warriors who possesed The Rare powerful Vaishnavastra of Shri Hari Vishnu. He slayed demon sambara with vaishnavastra. Narada gave him vaishnavastra on orders of Indra taking it from him.
Thereupon informed of his motive the king of gods said to Närada —“Do you soon approach the car of the large armed Pradyumna, make him conscious and remind him of his pristine birth. Give that of slayer of Asura this invincible coat of mail and Vaishnava weapons.”
Thereupon bending his bow and setting to it the Vaishnava arrow which Närada had brought, Keshava's son said:-“O arrow, if I am the son of Rukshmini begotten by Keshava do thou, on the strength of this truth, kill Shamvara in the battle-field.” Saying this the noble-minded Pradyumna, as if to consume the three worlds, drew his bow and shot the arrow at Shamvara. Thereupon that arrow, discharged by that Vrishni chief, piercing Shamvara's breast, entered into the earth. By the energy of that Vaishnava arrow all his flesh, bones, nerves, skull and blood were reduced to ashes.
3. Pradyumna was one of the few warriors who knew complete secret of chakravyuha.
Addressing Abhimanyu, that slayer of hostile heroes, who was not inferior to Vasudeva himself and whose energy was superior to that of Arjuna, the king said, 'O child, act in such a way that Arjuna, returning (from the Samsaptakas), may not reprove us. We do not know how to break the circular array. Thyself, or Arjuna or Krishna, or Pradyumna, can pierce that array. O mighty-armed one, no fifth person can be found (to achieve that teat).
4. Arjuna said he trusts only Pradyumna and Satyaki for protection of Yudhisthira.
Making over the monarch to thee, O mighty-armed one, or to that great car-warrior Pradyumna, I can go with an easy heart towards Jayadratha.
5. Pradyumna was Guru to Abhimanyu as well as Upapandavas in Dwarka.
And, O Krishna, as Rukmini's son is the preceptor of Aniruddha, of Abhimanyu, of Sunitha, and of Bhanu; so he is the preceptor and the refuge of your sons also! And a good preceptor, would unceasingly give them lessons in the wielding of maces and swords and bucklers, in missiles and in the arts of driving cars and of riding horses, being valiant. And he, the son of Rukmini, having bestowed a very good training upon them, and having taught them the art of using various weapons in a proper way, takes satisfaction at the valorous deeds of your sons, and of Abhimanyu.
6. Pradyumna's only arrows were powerful enough to defeat like of Kripa and karna and drona.
Kripa and Drona and Vikarna and Kama are not able to bear the keen arrows shot by Pradyumna.
7. Pradyumna accompanied Krishna and Balrama in banasur battle and defeated Lord Kartikeya in battle.
Kārtikeya was so strongly beaten by Pradyumna that he fled the battlefield, while the remnants of Bāṇāsura’s army, harried by the blows of Lord Balarāma’s club, scattered in all directions.
8. Pradyumna was a great illusionist. He had repulsed and destroyed strong illusions of Sambara and Shalva .
Sources:-
Harivamsa Chapter CCLII
Harivamsa Chapter CCLIII
Harivamsa Chapter CCLIV
Drona Parva: Abhimanyu-badha Parva: Section XXXIII
Drona Parva: Jayadratha-Vadha Parva: Section CX
Vana Parva: Markandeya-Samasya Parva: Section CLXXXII
Vana Parva: Tirtha-yatra Parva: Section CXX
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