The optimization process and recommendations:

1. Create Optimal Indexes (modified query below): The recommended indexes are an integral part of this optimization effort and should be created before testing the execution duration of the optimized query.
2. Prefer Inner Join Over Left Join (modified query below): We identified that one or more left joined entities (e.g. `tbl_Kategorie`) are used in the 'where' clause, in a way that allows to replace it with an optimized inner join. Inner joins can be fully optimized by the database, while Left joins apply limitations on the database's optimizer.
3. Prefer Inner Join Over Left Join (modified query below): We identified that one or more left joined entities (e.g. `tbl_Zbozi_VyslCena`) are used in the 'where' clause, in a way that allows to replace it with an optimized inner join. Inner joins can be fully optimized by the database, while Left joins apply limitations on the database's optimizer.
4. Use Numeric Column Types For Numeric Values (query line: 89): Referencing a numeric value (e.g. 8) as a string in a WHERE clause might result in poor performance. Possible impacts of storing numbers as varchars: more space will be used, you won't be able to perform arithmetic operations, the data won't be self-validated, aggregation functions like SUM won't work, the output may sort incorrectly and more. If the column is numeric, remove the quotes from the constant value, to make sure a numeric comparison is done.

Optimal indexes for this query:

ALTER TABLE `reg_SazbaDPH` ADD INDEX `reg_sazbadph_idx_sazbadphid` (`sazbaDPHId`);
ALTER TABLE `tbl_Kategorie` ADD INDEX `tbl_kategorie_idx_kategorieid_kategorieporadi` (`kategorieId`,`kategoriePoradi`);
ALTER TABLE `tbl_Kategorie` ADD INDEX `tbl_kategorie_idx_kategorieporadi` (`kategoriePoradi`);
ALTER TABLE `tbl_TypZbozi_VlastnostZbozi` ADD INDEX `tbl_vlastnostzbozi_idx_typzboziid` (`typZboziId`);
ALTER TABLE `tbl_VlastnostZboziHodnota` ADD INDEX `tbl_vlastnostzbozi_idx_vlastnostzboziid` (`vlastnostZboziId`);
ALTER TABLE `tbl_Vyrobce` ADD INDEX `tbl_vyrobce_idx_vyrobceid` (`vyrobceId`);
ALTER TABLE `tbl_Zbozi` ADD INDEX `tbl_zbozi_idx_zboziid_stavzboziid` (`zboziId`,`stavZboziId`);
ALTER TABLE `tbl_Zbozi_Kategorie` ADD INDEX `tbl_kategorie_idx_zboziid` (`zboziId`);
ALTER TABLE `tbl_Zbozi_VyslCena` ADD INDEX `tbl_vyslcena_idx_zbozivyslcenaskupinaid` (`zboziVyslCenaSkupinaId`);

The optimized query:

SELECT
        `_sd`.`sazbaDPHId`,
        `_sd`.`sazbaDPH`,
        `_sd`.`sazbaDPHProcent`,
        `_zk`.`zboziKategorieId`,
        `_zk`.`zboziId`,
        `_zk`.`kategorieId`,
        `_zk`.`zboziKategoriePoradi`,
        `_k`.`kategorieId`,
        `_k`.`kategorieNazev`,
        `_k`.`kategorieCelyNazev`,
        `_k`.`kategorieKod`,
        `_k`.`kategorieCesta`,
        `_k`.`kategoriePopis`,
        `_k`.`kategorieKeywords`,
        `_k`.`kategorieRodiceId`,
        `_k`.`kategoriePoradi`,
        `_k`.`kategorieSkryta`,
        `_k`.`kategorieVTopMenu`,
        `_v`.`vyrobceId`,
        `_v`.`vyrobceNazev`,
        `_v`.`vyrobceKod`,
        `_v`.`vyrobceKoeficient`,
        `_tzvz`.`typZboziVlastnostZboziId`,
        `_tzvz`.`typZboziId`,
        `_tzvz`.`vlastnostZboziId`,
        `_vzh`.`vlastnostZboziHodnotaId`,
        `_vzh`.`zboziId`,
        `_vzh`.`vlastnostZboziId`,
        `_vzh`.`vlastnostZboziHodnota`,
        `zvc`.`zboziVyslCenaId` AS `zvc_zboziVyslCenaId`,
        `zvc`.`zboziVyslCenaZboziId` AS `zvc_zboziVyslCenaZboziId`,
        `zvc`.`vyslCena` AS `zvc_vyslCena`,
        `zvc`.`vyslCenaSDPH` AS `zvc_vyslCenaSDPH`,
        `this`.`zboziId`,
        `this`.`zboziNazev`,
        `this`.`zboziKod`,
        `this`.`zboziIdentifikator`,
        `this`.`zboziPartNum`,
        `this`.`zboziEAN`,
        `this`.`zboziPopis`,
        `this`.`zboziOstatniParametry`,
        `this`.`zboziInterniInfo`,
        `this`.`zboziProdejniCena`,
        `this`.`zboziAkcniCena`,
        `this`.`zboziSetovaCena`,
        `this`.`zboziMocCena`,
        `this`.`sazbaDPHId`,
        `this`.`vyrobceId`,
        `this`.`typZboziId`,
        `this`.`stavZboziId`,
        `this`.`skladovaDostupnostId`,
        `this`.`zdrojCenId`,
        `this`.`zboziPHE`,
        `this`.`zboziAutorskyPoplatek`,
        `this`.`zboziVahovyPoplatek`,
        `this`.`nemenitStavZbozi` 
    FROM
        `tbl_Zbozi` AS this 
    LEFT JOIN
        `reg_SazbaDPH` AS _sd 
            ON this.sazbaDPHId = _sd.sazbaDPHId 
    LEFT JOIN
        `tbl_Zbozi_Kategorie` AS _zk 
            ON this.zboziId = _zk.zboziId 
    INNER JOIN
        `tbl_Kategorie` AS _k 
            ON _zk.kategorieId = _k.kategorieId 
    LEFT JOIN
        `tbl_Vyrobce` AS _v 
            ON this.vyrobceId = _v.vyrobceId 
    LEFT JOIN
        `tbl_TypZbozi_VlastnostZbozi` AS _tzvz 
            ON this.typZboziId = _tzvz.typZboziId 
    LEFT JOIN
        `tbl_VlastnostZboziHodnota` AS _vzh 
            ON this.zboziId = _vzh.zboziId 
            AND _vzh.vlastnostZboziId = _tzvz.vlastnostZboziId 
    INNER JOIN
        `tbl_Zbozi_VyslCena` AS zvc 
            ON this.zboziId = zvc.zboziVyslCenaZboziId 
    WHERE
        _k.kategorieId IN (
            155317, 5570, 155445, 5706, 5707, 155429, 155430, 155431, 5708, 5709, 5710, 155427, 155426, 155428, 11413, 5713, 5714, 5715, 5716, 5717, 5718, 5719, 5720, 10245, 10253, 11253, 10834, 10269, 10249, 10246, 10247, 10248, 5723, 5725, 5726, 5727, 5728, 5729, 155319, 5815, 5816, 5817, 5818, 5819, 5822, 5824, 5832, 11406, 11411, 11410, 11409, 6069, 6070, 6072, 6073, 6075, 6078, 6086, 11414, 6185, 155433, 6186, 6187, 6188, 6190, 6191, 6193, 6198, 6199, 6200, 6201, 6202, 6203, 6207, 6209, 11442, 6210, 6211, 6212, 6215, 6216, 6217, 6218, 6219, 6220, 155366, 6221, 11339, 11340, 11341, 11359, 6222, 6223, 6224, 6225, 6226, 6227, 6228, 11099, 155376, 6231, 6232, 6233, 6234, 6235, 6236, 155391, 155392, 155437, 6237, 6238, 6241, 6243, 6244, 6245, 6246, 6247, 6248, 6249, 6250, 6251, 6252, 6253, 6254, 6256, 6257, 6258, 6259, 6260, 6261, 10839, 155362, 6262, 6263, 6264, 6265, 155361, 6267, 6269, 11390, 11346, 11112, 11394, 11397, 155393, 6270, 11436, 10292, 6271, 6272, 6275, 6277, 6278, 6279, 6280, 6281, 11348, 10288, 11113, 6283, 6284, 6285, 6287, 155494, 11114, 6292, 6293, 6294, 6295, 6296, 6297, 6298, 6300, 6301, 6302, 6303, 6304, 11116, 6305, 10781, 6306, 6307, 6308, 6309, 6310, 6311, 6313, 6314, 6315, 6316, 6317, 6318, 6327, 6328, 155451, 6333, 6334, 6335, 6337, 6340, 6342, 6343, 6344, 6345, 6346, 11344, 11389, 10289, 10291, 10302, 10303, 10304, 10294, 10306, 10300, 10305, 10293, 10299, 10298, 10290, 10296, 10297, 11454, 11100, 11101, 11117, 131475, 11402, 5680, 5684, 5685, 5686, 5687, 5688, 5689, 11383, 5702, 5703, 5704, 5705
        ) 
        AND `this`.stavZboziId IN (
            2
        ) 
        AND zvc.zboziVyslCenaSkupinaId = '8' 
    ORDER BY
        _k.kategoriePoradi ASC LIMIT 18