Swami Sarvapriyananda while quoting Gita 2.14, 2.55-57, writes , "Events which would make most ordinary men miserable, leave him unshaken, for he sees the same inﬁnite Atman shining through (or, to put it in other words, events, fortunate or unfortunate, have no intrinsic reality apart from the Atman)". Can there be more elaboration on this? How to see the same Atman and how to not get shaken by difficulties?
Gita wants us to strive for evenness of mind.
Engage yourself in action with the mind steadfast in Yoga. Abandon attachments, O Arjuna, and be unperturbed in success and failure. This unperturbed sameness in all conditions is Yoga.
O Arjuna, mere action (with attachment) is far inferior to action done with the mind poised in evenness. Seek shelter in this state of unperturbed evenness (which can arise only in a desireless mind in communion with the Divine). Those who work for selfish gains are indeed pitiable.
One endowed with this unperturbed evenness of mind abandons the effects of both good and bad actions even here itself. Therefore, strive for this state of Yoga. Yoga is skill in action.
Such evenness of mind can occur only in a desireless mind which is in communion with divine. This state leads to sthita-prajna.
Definition of Sthita-prajna
O son of Pritha! When all the desires of the heart have been abandoned, and the Spirit finds joyous satisfaction in Itself (without dependence on any external factor) – then is one spoken of as a person of steady wisdom.
Whose mind is not agitated in adversity, who is free from desire, and who is devoid of attachments, fear and anger – such a person is called a sage of steady wisdom.
Whoever is without self-centered affection for anything, who rejoices not in favorable situations and hates not in unfavorable ones- such a person’s wisdom is firmly set.
When a person can withdraw his senses from their objects just like the tortoise its limbs on all sides, his wisdom is firmly set.
From the abstinent soul sense objects fall away, but not the taste for them. When the Supreme Truth is realized, even the taste departs.
How to see the same Atman and how to not get shaken by difficulties?
This can only be achieved through prolonged spiritual practices and reaching the state of vijnana.
Jnana and Vijnana
I consider that as knowledge (Jnana) by which one perceives, through all beings from Brahma to the ant, the continuing persistence of the causal categories – the groups of nine (Prakrti, Purusha, Mahattattva, Ahankara, and the five Tanmatras), the eleven (the five organs of action, the five organs of knowledge and the mind), the five (the five gross elements), and the three (the three Gunas) – and further sees that all these causal categories and their effects, the embodied beings, are interpenetrated by one Consciousness. Vijnana or immediate experience is this: In Jnana or contemplative experience one sees the presence of the one Substance persisting through numerous changing modes. When the permeating Substance alone is seen to the exclusion of all changing modes apprehended as different from It, then that understanding is called Vijnana. One should perceive all these modes of the triune Gunas as originating, subsisting and dissolving (in and by that Substance alone). Only that which thus persistently continues in a series of effects passing from one to the next without discontinuity, and remains the same at the end of the series as it was at the beginning, that alone is the essence (Sat).
Srimad Bhagavata Purana XI.19.14-16
One acquires evenness of mind and sees the Atman everywhere in the state of vijnana.
Acharya Shankara in Katha Upanishad 2.2.11 writes,
Seeing that if one be the atman of all, he may be regarded as subject to the grief of samsara, this is said. As the sun benefiting the eye by its rays and manifesting even unclean things such as urine, ordure, etc., though being the eye of all, the world seeing them is not tainted with sins and other blemishes due to seeing unclean things, etc., and by stains caused by physical contact with unclean objects so the one internal atman is not tainted with the misery of the world, being outside that; for, the world by ignorance superposed on the atman, suffers misery arising from desire and karma. But that is not really in the atman, just as, the serpent, silver, water and dirt superposed on the rope, mother-of-pearl, barren spot and the sky, respectively, do not really exist as blemishes in the rope, etc.; from the superposition, by false notion, they are perceived as blemishes in the true objects connected (by the notion); the true objects are not tainted by such blemishes because they are external to the false notion so superposed. Thus the world having superposed on the atman, the false notion of deed, agency and fruits like the notion of the serpent (on the rope), suffers the misery of birth, death, etc., due to that. But the atman, though the atman of all the world, is not tainted by the misery of the world arising from the superposition of a false notion. Why? being external. Because he is like the rope, etc., external to the false notion superposed on him.