In the fast ignition (FI) scheme, at first high density fuel core plasma is assembled by an implosion laser and then heated by a peta watt laser to achieve the fusion burning condition. A typical target for FI is a shell fitted with a re-entrant Au cone to keep a path for the heating laser clean. Recently, for the FIREX-I scale size experiment, the CH tip of the guiding cone has advantages from the viewpoint of the generation of hot electrons and hot electron transport. As a result, from the viewpoint of implosion dynamics, cone-guided implosion with the CH tip is studied using the two-dimensional radiation hydrodynamic code. Two shockwaves caused by the leading shock of implosion and jet from the core determine the breakup time of the tip. With a sophisticated target and laser pulse shape design, CH, CD or other low-Z material tips will be realized without breaking up the cone tip before the maximum compression timing and debasement of the implosion performance.