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The Garuḍa Purāṇa lists some garuḍa-mṛtyu-rakṣa mantra in the following śloka.

ॐ अमृतेश्वर ॐ भैरवाय नमः।
एवं ॐ जुं हंसः सूर्याय नमः॥ १।१८।१९॥
om amṛteśvara om bhairavāya namaḥ |
evaṁ om juṁ haṁsaḥ sūryāya namaḥ || 1|18|19 ||

Step-1: The first step to strengthen the Lagna with the first mantra. This is common for everyone and firmly establishes the oṁkāra on the ascendant.

ॐ अमृतेश्वर ॐ भैरवाय नमः।
om amṛteśvara om bhairavāya namaḥ
MantraAdvanced

Step-2: Once this is done then all evils are under check and the second mantra is to be used to protect the soul. The second mantra is a combination of the Kahola ṛṣi Mṛtyuṅjaya bīja mantra ‘om juṁ saḥ’ and the mantra for chara ātmakāraka. The mantra takes the form ‘om juṁ haṁsaḥ sūryāya namaḥ’ for one who is born with Sun as chara ātmakāraka.

एवं शिवाय कृष्णाय ब्रह्मणे च गणाय च।
चण्डिकायै सरस्वत्यै महालक्ष्मादि पूजयेत्॥ १।१८।२०॥
evaṁ śivāya kṛṣṇāya brahmaṇe ca gaṇāya ca |
caṇḍikāyai sarasvatyai mahālakṣmādi pūjayet || 1|18|20 ||

For other planets as chara ātmakāraka another seven deities have been mentioned in the Garuḍa Purāṇa. The eight specifically mentioned for eight chara ātmakāraka are – Sūrya, Śiva, Kṛṣṇa, Gaṇa (Gaṇeśa), Brahma, Caṇḍīkā, Sarasvatī and Lakṣmī. The mantras are listed below. It is important that the correct mantra should be chosen for the planet which is chara ātmakāraka. These mantra remove every poison in the system and restore health.

Sun as Ātmakāraka
ॐ जुं हंसः सूर्याय नमः।
om juṁ haṁsaḥ sūryāya namaḥ|

Jupiter as Ātmakāraka
ॐ जुं हंसः शिवाय नमः।
om juṁ haṁsaḥ śivāya namaḥ|

Mercury as Ātmakāraka
ॐ जुं हंसः कृष्णाय नमः।
om juṁ haṁsaḥ kṛṣṇāya namaḥ|

Saturn as Ātmakāraka
ॐ जुं हंसः ब्रह्मणे नमः।
om juṁ haṁsaḥ brahmaṇe namaḥ|

Mars as Ātmakāraka
ॐ जुं हंसः गणाय नमः।
om juṁ haṁsaḥ gaṇāya namaḥ|

Rāhu as Ātmakāraka
ॐ जुं हंसः चण्डिकायै नमः।
om juṁ haṁsaḥ caṇḍikāyai namaḥ|

Moon as Ātmakāraka
ॐ जुं हंसः सरस्वत्यै नमः।
om juṁ haṁsaḥ sarasvatyai namaḥ|

Venus as Ātmakāraka
ॐ जुं हंसः महालक्ष्म्यै नमः।
om juṁ haṁsaḥ mahālakṣmyai namaḥ|

Further refinement of the mantra has been allowed with the use of the word ‘ādi’ in ‘mahālakṣmādi’ meaning that very subtle and specific forms can be deciphered from the chart.

Illustration:
karakamsa_sr

Saturn is the chara ātmakāraka in this chart and the regular mantra should have been the one for Brahma, the deity of Saturn (Parāśara). However, we can take into consideration the fact that Saturn is also the dispositor of the natal Moon and becomes śubhapati (Moon dispositor) for the chart. This special status of the śubhapati becoming ātmakāraka is called ‘Kevala’ (Jaimini Upadeśa). The particular form of Brāhmaṇa transforms to Atri (Maharṣi – sire of the Moon) and the mantra transforms as follows –

Saturn as Kevala Ātmakāraka

ॐ जुं हंसः अत्रिब्रह्मणे नमः।
om juṁ haṁsaḥ atribrahmaṇe namaḥ

However, in this chart, a second level transformation has occurred as the ātmakāraka planet is also placed in its own sign. The devatā is no longer considered from the graha Saturn (Brahma) but instead from the vāyu tattva (Parama Śiva). To this add the fact of the Moon being disposited by Saturn and the specific subtle form is a lunar form – Śrī Somanāth Śiva.

Tattva level transformations occur when any of the eight planets, as ātmakāraka is also placed in own sign. Sun and Mars = Āditya; Moon and Venus = Durgā; Mercury = Mahā Gaṇeśa; Jupiter = Mahā Viṣṇu; Saturn = Parama Śiva (Iśvara). Thus the mantra undergoes another more subtle transformation to Śrī Somanāth.

ॐ जुं हंसः सोमनाथाय नमः।
om juṁ haṁsaḥ somanāthāya namaḥ|