Those big spikes at just after 1 minute and around 1:30 are close to 0 dB and so prevent the Amplify effect from making the track louder without clipping those spikes.
What you could do is to use a “limiter” to limit those spikes to say -6 dB, which would then allow the track to be amplified by an additional 6 dB without clipping.
There is a plug-in called “Brick Wall Limiter” that will do both the “limiting” and the amplification in one step. It is available here: https://forum.audacityteam.org/t/peak-limiter/20300/1
Instructions for installing plug-ins: http://wiki.audacityteam.org/wiki/Download_Nyquist_Plug-ins#Installing_Plug-ins
Try the Brickwall limiter with left and right set to 6 and the “hold” at the default setting.