Attosecond Science aims at studying ultrafast dynamics of electronic processes on a timescale of less than a femtosecond. Observing the electronic motion is done so far using attosecond bursts of XUV light issued from the interaction of a controlled laser light field with a gas medium at moderate intensity. The project ALPINE aims at scaling waveform-controlled laser-matter interaction to relativistic intensity, in order to generate isolated attosecond light pulses of unprecedented brightness. At such intensity, the laser electric field completely ionizes the interaction media and creates a plasma mirror which oscillates at speed of light and radiates very bright XUV pulses of attosecond duration. I will explore this generation mechanism by using a unique laser system (Light Wave Synthesizer 20) delivering two-cycle pulses with 20 TeraWatt peak power. Preliminary studies will provide the ideal interaction parameters, in terms of laser characteristics and plasma mirror shaping, in order to maximize the energy contained in the attosecond emission. I will then focus on measuring and stabilizing the laser waveform with sub-cycle accuracy, to ensure shot-to-shot stability and control of the attosecond pulses. Finally I will explore different regimes of interaction aiming at generating intense isolated attosecond pulses, like intensity gating and lighthouse technique. In parallel of this work I will perform studies to develop innovative targets with attosecond stability, with a view toward future applications of this ultra-bright isolated attosecond source.