High Field Vertical Magnet Test Facility (HFVMTF) is a joint project between the Office of High Energy Physics (HEP) and the Office of Fusion Energy Sciences (FES). Its construction is currently under way at Fermi National Accelerator Laboratory (Fermilab). As a part of the project a new double bath superfluid helium cryostat has been designed. The cryostat can accommodate magnets with up to 20 tonne weight and 1.3 m diameter. This paper discusses challenges and solutions for cryostat, lambda plate and heat exchanger design, and presents results of performance analysis.