I think that you have to use the following chapter

Davids, Barbara J., and Frances D. Gillin. Methods for giardia culture, cryopreservation, encystation, and excystation in vitro. Springer Vienna, 2011.

The cysts were purified from human faeces, according to the technique of Thompson-Roberts et al. (1976). This technique is based on the separation of cysts through a sucrose gradient. Feces diluted with water at a ratio of one to five parts of water was filtered through cheesecloth and centrifuged four folds for five minutes at 2500 rpm. The pellet was washed four times by centrifugation in order to remove excess debris, resuspending the final pellet in water. Then we proceeded to the first fractionation, placing it in a tube, a solution of 1 M sucrose, feces and on asuspensão This material centrifuging at 1500 rpm for 20 minutes. Cysts located in sucrose-water interface were carefully collected, transferred to a centrifuge tube of 15 ml by adding water and centrifugation at 2500 rpm for 10 minutes. The pellet obtained was resuspended in 3 ml of water to make the second fractionation, placing it in a centrifuge tube with a capacity of 15ml, 3 ml of a 0.75 M sucrose solution, and on this, 3 ml suspension of cysts. After centrifugation at 1500 rpm for 10 minutes, the cysts were removed from the sucrose-water interface, resuspended in water and washed twice with water to remove the sucrose. The purified cysts containing pellet was resuspended in 1 ml of water for counting cysts in blade with the average of ten campos.Após was made axenização, desencistamento and cultivation. For axenização, desencistamento and cultivation techniques described below were performed: after checking the viability of isolated cysts, began the process of axenização in order to become free samples of bacterial flora and fungi associated. The cysts were treated initially with a solution of HCl 1-2%, for two days at 4 ° C, or directly with amikacin (100 mg / ml) and nystatin (10.000UI / ml). Then they were washed with phosphate buffered saline (PBS), pH 7.2, making a new assessment of feasibility to induce desencistamento according to the technique of Bingham & Meyer (1979) with some adaptations, and the technique Feely et al. (1991). Bingham & technique in Meyer (1979), with some adaptations, the cysts were initially submitted to a solution of HCl at pH 0.5, pH 2.0 and pH 4.5 at 37 ° C for 5, 10 and 15 min ., respectively, under stirring, in a ratio of one part of the solution of the nine shares cistospara HCl solution. Then, the material was centrifuged at 2500 rpm / 5 min., Ignoring all HCl solution, and the pellet was resuspended in PBS (pH 7.2). The material was washed three times with PBS (pH 7.2) for total elimination of HCl. Was also used for desencistamento, the technique of Feely et al. (1991), in which is added a potassium phosphate buffer solution to a 0.1 M solution 0.3M sodium bicarbonate, to obtain a pH of 7.5, this is the induction medium in which the incubated cysts in centrifuge tube 15 rpm for five minutes After centrifuging at 3277 rpm for five minutes, washed in 15 ml of potassium phosphate buffer pH 7.0, concentrated by centrifugation again 5 min. to 3277rpm, resuspending in 1 to 2 ml saline (0.85%) and incubated at 37 ° C for subsequent determination desencistamento rates of 5, 15 and 30 minutes. Pellets were seeded in tubes with screw caps (16 x 120 mm) containing 12ml of TYI-S-33 modified (10), plus 1 mg / ml of ofloxacin and 100 IU / ml nystatin, being kept in the greenhouse bacteriological , 35.5 - 37 ° C, in the tilted position. The tubes were examined daily in microscópioinvertido with 100X, for the presence of trophozoites. Those positive, with trophozoites adhere to the wall were placed in an ice bath for 15 min., Inverted several times to the detachment of trophozoites making it aseptically to a tube containing subculture to fresh medium. In tubes which trophozoites were few, instead of the spike, the medium replacement was carried out, ie the replacement of old medium with fresh medium.

I concur with the protocols recommended by Harith and Walter. In my experience, you can try for excystation a first step with double-distilled water at pH 2.0 and incubation times of 15, 30 and 45 minutes at 37oC (if cysts were purified from feces 30 and 45 minutes are good) followed by transfering cells to TYI-S-33 médium.

I have experience in axenic Giardia culture. I attach file with scans of two our articles concenrning axenic growth of Giardia. There are detailed protocols of Giardia cysts purification and excystation, as well as axenic culture.

pencillin streptomycin is also good. we are using those

Dear Mosaab,

My advice regarding the cultivation of Giardia is to seek commercial culture media. You can obtain these lyophilized media from ATCC together with quality reference strains. 

Kind regards,

Rashad

Dear Professors and Doctors, thank you all very much for your valuable information's, really very helpful