Is there any way to change from a tourist visa to a work visa to apply for a temporary residence card or is it required to get a work visa?

Regarding the issue you raised, at Article 7 of the Law on Entry, Exit, Transit, and Residence of Foreigners in Vietnam 2014 modified by Clause 2, Article 1, Law on Entry, Exit, Transit, and Residence of Foreigners in Vietnam, amended 2019 regulations:

“Article 7. Form and validity of visa

...

3. Visa is valid once or multiple times; Electronic visas and visas issued for the cases specified in Point b, Clause 2 of this Article are valid once.

4. Visa purposes cannot be changed, except in the following cases:

a) Have documents proving that you are an investor or representative of a foreign organization investing in Vietnam according to the provisions of Vietnamese law;

b) Have documents proving the relationship as father, mother, wife, husband, child with the inviting or sponsoring individual;

c) Invited or sponsored by an agency or organization to work and have a work permit or confirmation that they are not subject to a work permit according to the provisions of labor law;

d) Enter with an electronic visa and have a work permit or confirmation that you are not subject to a work permit according to the provisions of law..."

At the same time, at Article 8 etArticle 9 of the Law on Entry, Exit, Transit, and Residence of Foreigners in Vietnam 2014 modified by Point e Clause 3,Point c Clause 4 Article 1 Law on entry, exit, transit, and residence of foreigners in Vietnam amended 2019 also stipulates as follows:

"Article 8. Visa symbol

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16. LĐ1 - Issued to foreigners working in Vietnam with confirmation that they are not subject to a work permit, unless an international treaty to which Vietnam is a member has different provisions.

17. DL - Issued to people going on vacation.

"Article 9. Visa duration

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2. Visas with symbols HN and DL are valid for no more than 3 months.

...

5. Visas labeled LD1, LD2 are valid for no more than 02 years."

Thus, in terms of visa regulations, different symbols will be used for different purposes and you are not allowed to change the purpose of the visa.

If your boss only has a tourist visa, the validity of this visa is only 3 months and you are not allowed to use this visa to apply for a temporary residence card.

If you want to apply for a temporary residence card, you must have a work visa (the purpose of entering Vietnam is to work, not to travel). In this case, I will not be able to change my visa, the only way is to return home and apply for a visa again for the purpose of working.