Is there any act in Islam that a Muslim can do, whether a saying or deed, so as to enter Paradise whenever he wants, other than that of martyrdom in battle?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.

Entering Paradise, the residence of honor for the obedient servants of Allaah The Almighty, is a sublime rank which cannot be attained by mere aspiration or longing; rather, it is attained through doing righteous deeds which Allaah The Almighty Accepts by His favor.

Allaah The Almighty Says (what means): {And that is Paradise which you are made to inherit for what you used to do.} [Quran 43:72] Ibn Katheer said, "The verse means that your deeds were the reason for being endowed with the mercy of Allaah, because surely no one enters Paradise by virtue of his deeds only, but by the mercy and favor of Allaah. However, the degrees vary according to people's righteous deeds."

It was narrated on the authority of Abu Hurayrah that the Prophet said: "He who fears (not reaching the satisfaction of Allaah), hastens to perform acts of obedience, and he who hastens to perform acts of obedience attains the (sublime) degree. Surely, the merchandise of Allaah is precious. Surely, the merchandise of Allaah is Paradise". [At-Tirmithi] [Al-Albaani: Saheeh]

Furthermore, there is no way through which a Muslim can enter Paradise at the time he chooses for two reasons:

The first is that man's death is not subject to his own will or choice; it only happens when his life ends according to what Allaah The Almighty has decreed for him since he was a fetus in his mother's womb.

The second is that a person cannot be sure that he will be from the people of Paradise, as the last deeds of a person before his death are in the Hands of Allaah The Almighty.

The Prophet said:

"(The matter of the creation of) a human being is put together in the womb of the mother in forty days, and then he becomes a clot of thick blood for the same period, and then a piece of flesh for the same period. Then Allaah sends an angel who is ordered to write four things. He is ordered to write down his (i.e. the new creature's) deeds, his sustenance, his (date of) death, and whether he is destined to be of the wretched or happy. Then the soul is breathed into him. So, a man amongst you may do (good deeds) until there is only a cubit between him and Paradise and then what has been written for him decides his behavior and he starts doing (evil) deeds of the people of Hell. Similarly, a man amongst you may do (evil) deeds till there is only a cubit between him and Hell, and then what has been written for him decides his behavior, and he starts doing deeds of the people of Paradise.” [Al-Bukhari and Muslim] This is the narration of Al-Bukhari .

Allaah Knows best.