This happens because of dependencies which need backporting. You are not alone with this problem, so really this new Aria2 version is available in compiled deb packages from two Rob Savoury's PPAs:
Adding any of these PPAs to the system will cause upgrade of many packages to new versions. If you are sure with walking this way - use commands below:
sudo add-apt-repository ppa:savoury1/backports
sudo apt-get update
sudo apt-get install aria2 --only-upgrade
Then you will have two choices:
Upgrade all other packages using just added PPA by
sudo apt-get dist-upgrade
Remove the just added PPA keeping most of the packages at their current 18.04 LTS versions while having newest Aria2 by
sudo add-apt-repository -r ppa:savoury1/backports
To keep system manageable I would recommend to use latter method.
If you do not want to add the PPA, you have to download aria2 package with its dependencies manually and install them by commands below
cd ~/Downloads
wget -c https://launchpad.net/~savoury1/+archive/ubuntu/backports/+files/aria2_1.36.0-1~18.04.sav0_amd64.deb
wget -c https://launchpad.net/~savoury1/+archive/ubuntu/backports/+files/libaria2-0-dev_1.36.0-1~18.04.sav0_amd64.deb
wget -c https://launchpad.net/~savoury1/+archive/ubuntu/backports/+files/libaria2-0_1.36.0-1~18.04.sav0_amd64.deb
wget -c https://launchpad.net/~savoury1/+archive/ubuntu/backports/+files/libgnutls30_3.7.3-4ubuntu1~18.04.sav0_amd64.deb
wget -c https://launchpad.net/~savoury1/+archive/ubuntu/backports/+files/libnettle8_3.7.3-1~18.04.sav0_amd64.deb
wget -c https://launchpad.net/~savoury1/+archive/ubuntu/backports/+files/libtasn1-6_4.18.0-4~18.04.sav0_amd64.deb
wget -c https://launchpad.net/~savoury1/+archive/ubuntu/backports/+files/libhogweed6_3.7.3-1~18.04.sav0_amd64.deb
wget -c https://launchpad.net/~savoury1/+archive/ubuntu/encryption/+files/libp11-kit0_0.23.20-1ubuntu0.1~18.04.sav0_amd64.deb
sudo apt-get install ./aria2_1.36.0-1~18.04.sav0_amd64.deb ./libaria2-0-dev_1.36.0-1~18.04.sav0_amd64.deb ./libaria2-0_1.36.0-1~18.04.sav0_amd64.deb ./libgnutls30_3.7.3-4ubuntu1~18.04.sav0_amd64.deb ./libnettle8_3.7.3-1~18.04.sav0_amd64.deb ./libtasn1-6_4.18.0-4~18.04.sav0_amd64.deb ./libhogweed6_3.7.3-1~18.04.sav0_amd64.deb ./libp11-kit0_0.23.20-1ubuntu0.1~18.04.sav0_amd64.deb