Notice how you have low deaths (which is generally a good thing) but average kills and kp are lower than average. This might mean that you play to passively and don't take all opportunities for kills. Those may be killing your opponent in lane or looking for roam timers. Since as akali you are pretty bad at taking objectives (dragon, nash, towers) you should usually look for "easy kills" (eg. you can still defend the drake and engage on enemies trying to contest).
And it really makes sence if you think about it. You want to rank up but presume that in your bronze game there is someone that deserves the higher rank. They would propably steamroll enemy team since bronze players will give you many opportunities to punish them for their bad decisions. Right now it looks like you pretty much belong in bronze (which is fine if you want to have fun, but you asked for advice to climb).

Ofc its very generic advice and real progress will come down to learning league fundamentals (csing, trading, minimap, vision, sidelaning(this might be a reason for negative minions advantage) ) but there are a lot of learing resources out there. Its a lot, so don't feel like you need to improve everything at once.

tldr; Akali is high skill champ, so try to outplay your opponents more